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partnership

IntroDUCtIon

In partnership, two or more persons carry on a business and

sharetheproitsofthebusinessatanagreedproportion.Persons who have entered into partnership with one

another are individually called partners and collectively

called a fi rm. The name under which their business is

carried on is called the fi rm name. The partnership may

be simple or compound type.Simple Partnershipisoneinwhichthecmesapitalof

eachpartnerisinvestedinthebusinessforcertaintimespan.

Compound Partnership is one in which the capitals

of the partners are invested for different time periods.Again, a partner may be a working partner or a

sleeping partner.A Sleeping Partner is one who invests the capital

in the business, but does not actively participate in the

day-to-day activities of the business.A Working Partnerbesidesinvestingcapital,takes

part in running the business. For hiswork, he is eitherpaid certain amount of salary and also share of proit.

1. (a) If capitals of two partners be `C1 and

`C2 for the same period and the totalproitbe`P, thensharesof thepartnersin the proit are

`

C P

C C

1

1 2

×+

and `C P

C C

2

1 2

×+

.

(b) If the capitals of threepartners be`C1,

`C2 and `C3 for the same period, andthetotalproitbe`P,thensharesofthepartners in the proit are

` `C P

C C C

C P

C C C

1

1 2 3

2

1 2 3

×+ +

×

+ +

,

and `C P

C C C

3

1 2 3

×+ +

.

Illustration 1: A, B and C invested `20,000, `50,000

and `40,000, in a business. The net proit for the yearwas `12,100.ThisT which was divided in proportion to

investments.Findout theamountofproiteachpartnerhas earned.Solution: We have, C1 = 20,000, C2 = 50,000, C3 = 40,000

and P =12,100.

Therefore, proit share ofA:

= C P

C C C

1

1 2 3

×+ +

= 20 000 12 100

20 000 50 000 40 000

, ,

, , ,

×+ +

= 2

1112 100× , = `2,200.

Proit share ofB:

= C P

C C C

2

1 2 3

×+ +

= 50 000 12 100

20 000 50 000 40 000

, ,

, , ,

×+ +

= 5

1112 100× , = `5,500.

Proit share ofC:

= C P

C C C

3

1 2 3

×+ +

= 40 000 12 100

20 000 50 000 40 000

, ,

, , ,

×+ +

= 4

1112 100× , = `4,400.

8

soME BasIC ForMUlaE

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Copyright © 2017 Pearson India Education Services Pvt. Ltd

Chapter 88.2

2. (a) If the capitals of two partners be `C1

and `C2 for the periods t1 and t2, and

the totalproitbe`P, thensharesof thepartners in the proits are:

`C t P

C t C t

1 1

1 1 2 2

× ×+

and `C t P

C t C t

2 2

1 1 2 2

× ×+

(b) If the capitals of three partners be `C1,

`C2 and `C3fortheperiodst1, t2 and t3,

respectively, and the total proit be `P,

then shares of the partners in the proitare

` `C t P

C t C t C t

C t P

C t C t C t

1 1

1 1 2 2 3 3

2 2

1 1 2 2 3 3

× ×+ +

× ×

+ +

, ,

and `C t P

C t C t C t

3 3

1 1 2 2 3 3

× ×+ +

Illustration 2: AandB are twopartners in a business.Acontributes `1,200for5monthsandBcontributes`750for4months.Iftotalproitis`450,indouttheirrespectiveshares.Solution: We have, C1 = 1200, C2 = 750, t1 = 5, t2 =

4 and P = 450.∴ Proit share ofA

= C t P

C t C t

1 1

1 1 2 2

1 200 5 450

1 200 5 750 4

× ×+

=× ×

× + ×

,

,

= 27 00 000

9 000

, ,

, = `300.

Proit share ofB

= C t P

C t C t

2 2

1 1 2 2

× ×+

= 750 4 450

1 200 5 750 4

× ×× + ×,

= 13 50 000

9 000

, ,

, = `150.

1. (a) Ifthecapitalsoftwopartnersbe`C1 and

`C2fortheperiodst1 and t2 respectively,

then

Profit of A

Profit of B=

×

×

C t

C t

1 1

2 2

.

(b) If the capitals of three partners be `C1,

`C2 and `C3 for theperiods t1, t2 and t3

respectively, then proit of A: proit ofB: proitofC=C1 × t1:C2 × t2:C3 × t3.

Note:

Ifthereisalossinthebusiness,then LossofA:LossofB : LossofC = C1 × t1:C2 × t2:C3 × t3.

Illustration 3: There are three partners A, B and C

in a business.A invests `2000 for 5months,B invests

`1200 for6monthsandC invests `2500 for3months.Find out the ratio of their shares in the proit.Solution: Here, C1 × t1 = 2,000 × 5 = 10,000, C2 × t2

=1,200×6=7,200 andC3 × t3 = 2,500×3=7,500.∴ Proit ofA: Proit ofB: Proit ofC

= C1 × t1:C2 × t2:C3 × t3 = 10,000:7,200:7,500 or 100:72:75.

2. If the capitals of three partners in a businessinvested in the ratio of C1:C2:C3 and their

proitsareintheratioP1:P2:P3, then the ratio

of timingof their investments = P

C

P

C

P

C

1

1

2

2

3

3

: : .

Illustration 4: Anu, Manu and Tanu invested capitals

inabusinesstheratio4:6:9.Attheendofthebusiness,theyreceivedtheirsharesofproitsintheratio2:3:5.Findthe ratioof time forwhich they invested their capitals.

Solution: We have C1:C2:C3 = 4:6:9

and P1:P2:P3 = 2:3:5

Therefore, the ratio of time for whichAnu,Manuand Tanu invested their capitals

=

=

P

C

P

C

P

C

1

1

2

2

3

3

2

4

3

6

5

9

: :

: :

or, 1

2

1

2

5

9: :

or, 9:9:10.

soME UsEFUl sHortCUt MEtHoDs

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8.3Partnership

3. Three partners invested their capitals in abusiness. If the timingof their investments isin the ratio of t1:t2:t3, and their proits are inthe ratio of P1:P2:P3, then the ratio of their

capitals invested is P

t

P

t

P

t

1

1

2

2

3

3

: : .

Illustration 5: Gupta, Singhal and Kansal starts abusiness.Iftheratiooftheirperiodsofinvestmentsare1:2:5and theirproitsare in the ratioof3:4:5,ind theratio of capitals ofGupta, Singhal andKansal.

5. A startsbusinesswithaninvestmentof`3500.Fivemonths later B joins A as a partner. After a year,theproitsaredividedintheratioof2:3.Howmuchdid B contribute?

(a) `7,000 (b) `11,000

(c) `9,000 (d)Noneof these 6. Gupta and Bansal enters into a partnership with their

capitals in the ratio 5:6. At the end of 8 months,Gupta withdraws his capital. If they receive theirshares proits in the ratio of 5:9, ind out how longBansal’s capital was invested in the business?

(a) 10 months (b) 12 months

(c) 14months (d)Noneof these 7. Arvindbeganabusinesswith`550.Later,Brijwith

`330.WhendidBrij join if theproit at the endofthe year was divided in the ratio 10:3?

(a)After 4months (b)After 6months(c)After 4.5months (d)Noneof these

8. A began a businesswith`3750.Later,with`5000.WhendidBjoiniftheproitsattheendoftheyearwas divided equally?

(a)After 5months (b)After 9months(c)After 7months (d)Noneof these

9. Anju and Brijesh enters into a partnership with their

capitals in theratioof5:9.At theendof8months,Anju withdraws her capital. If they receive theirshareofproitintheratioof4:9,indouthowlongBrijesh’s capitalwas invested in thebusiness.(a) 8months (b)10months(c) 12months (d)Noneof these

10. A,B andC invested capitals in the ratio 3:5:9; thetimingof their investmentsbeing in the ratio2:3:1.Inwhat ratiowould their proits bedistrubuted?

Solution: We have, P1:P2:P3 = 3:4:5

and t1:t2 :t3 = 1:2:5.

∴ The required ratio = P

t

P

t

P

t

1

1

2

2

3

3

: :

= 3

1

4

2

5

5: : or 3:2:1

Thus, Gupta, Singhal and Kansal invested theircapitals in the ratio of 3:2:1.

1. NikitaandNishitaentersintoapartnershipbyinvesinvesting `50,000 and `40,000, respectively. Theyagreed to share proits in the ratio of their capitals.Find out the share of Nikita when proit of thebusiness is `22500 after a year.(a) `1,500 (b) `9,500(c) `10,500 (d)Noneof these

2. Niki, Nisha and Anu formed a partnership withinvestments of `75,000, `60,000 and `40,000,

respectively.After3yearsofoperation,thepartnershipearnedanetproitof`26,250.WhatwastheshareofAnu in theproit?(a) `6,000 (b)`5,000

(c) `8,000 (d)Noneof these

3. Mahesh,SureshandGaneshenteredintoapartnership.partnershipbusiness.Maheshinvested`16,000for9months. Suresh invested `12,000 for 6months andGanesh invested `8,000 for 12months. At the endof a year, there was a proit of `26,000. Find outthe share ofSuresh in theproit.(a) `8,000 (b)`7,500

(c) `6,000 (d)Noneof these 4. SitaandGitaentersintoapartnership.Sitacontributes

`5,000 while Gita contributes `4,000.After1month,

Gita withdraws 1

4partofhercontributionandafter

3 months Sita invests `2,000 more. When Gita

withdraws her investment, at the same time, Rita

joins them by investing `7,000. If at the end of 1year there is a proit of `1,218,whatwill be shareofRita in theproit?(a) `488.47 (b)`8,447.37(c) `588.47 (d)Noneof these

ExErcisE-1

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Chapter 88.4

(a) 2:5:3 (b) 3:2:5

(c) 7:5:3 (d)Noneof these 11. Sumit,PunitandRamitstartedabusinessbyinvesting

theircapitals intheratioof1:2:3.Attheendofthebusiness term, they received their shares of proitin the ratio of 1:2:3. Find out the ratio of time forwhich they invested their capitals.(a) 1:1:1 (b) 2:3:4

(c) 2:4:3 (d)Noneof these 12. A, B and C starts a business. If the ratio of their

periodsofinvestmentsare2:3:6andtheirproitsarein the ratioof4:5:6, then the ratioofcapitalsofA,B and C is:

(a) 6:8:10 (b)12:10:6(c) 10:12:6 (d)Noneof these

13. A,BandCrentedapasture.Aputs in12oxenfor6 months, B 8 oxen for 7 months and C 6 oxenfor 8months. If the rent of the ield is `396,whatamount of rentwaspaidbyA?(a) `126 (b)`108(c) `162 (d)`168

14. A, B,CandDenters intopartnership.Acontributes1

3of thecapital,Bcontributes 1

4, C contributes

1

5

and D contributes the rest. What is the share of Dwhenproit is`6000?(a) `2000 (b) `1600(c) `1200 (d) `1300

15. A and B enters into a partnership for a year. Acontributes `1500 and B `2000.After4months,theyadmits C who contributes `2250.IfBwithdrawshiscontribution after 9months, at the end of the yearthey share proit in the ratio:(a) 2:1:3 (b) 1:3:2

(c) 1:1:2 (d) 1:1:1

16. A and B started a business with initial investments in

theratioof5:7.If,afteroneyear, theirproitswereintheratioof1:2andtheperiodforA’sinvestmentwas for 7months,B invested themoney for:

(a) 6months (b)21

2 months

(c) 10 months (d) 4 months

17. A and B jointly invests `2100 and `3100 in airm. Aisanactivepartner,hencehereceives25%oftheproit separately. If their business yields `1040 as

proit,whatwillbetheproitshareforeachofthem?(a) `415, `625 (b)`575, `465(c) `515, `525 (d) `560,`480

18. Two partners invested `12500 and `8500 in abusiness, They decided that 60% of the profitincurred from the business will be equally dividedbetweenthemwhileremainingproitwillbeassumedas interest on their capitals. If one of the partnersreceives `300moreproitthantheother,whatisthetotal proit in thebusiness?

(a) `3937.50 (b)`4940.50(c) `3936.50 (d)`4156

19. A, B, C enters into a partnership with shares in the

ratio 7

2

4

3

6

5: : .After4months,Aincreaseshisshare

by50%.If thetotalproitat theendofoneyearbe`21600, thenB’s share in theproit is:

(a) `2100 (b) `2400

(c) `3600 (d)`4000

20. A andB invests inabusiness in the ratioof3:2. If5%of the totalproitgoes tocharityandA’s shareis `855, then total proit is:

(a) `1576 (b)`1537.50(c) `1500 (d) `1425

21. InabusinessBasleepingpartnerandAisaworkingpartner. A invests `5000 and B invests 6000. A

receives 121

2%ofproit formanaging thebusiness

and the remaining amount is divided in propoftionto their capitals. A’s share of proit in a proit of`880 is:

(a) `350 (b) `400

(c) `420 (d) `460

22. A starts businesswith a capital of `1200.B andCjoin with some investments after 3 and 6 months,respectively. If, at the end of a year, the proit isdividedintheratioof2:3:5,whatisB’sinvestmentin the business?

(a) `2400 (b) `1800(c) `3600 (d)`6000

23. A, B and C entered into a partnership with `35,12,420,

`42,22,180and`40,65,400.After2years,Awithdrew`11Lakhs.At the same time,C invested`8Lakhsmore. If at the endof3years, proit is`10,53,000,

what is the share ofC in theproit?

(a) `283,117.80 (b)`379,996.20(c) `399,866 (d)`299,866(e)Noneof these

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8.5Partnership

24. A and B enters into a partnership. A supplieswhole of the capital amounting to `45000 with the

conditionthattheproitsaretobeequallydistributedand thatB paysA interest on half of the capital at10% per annum, but receives, `120 per month forcarryingontheconcern.WhenB’sincomeis1/2ofA’s income, their total yearly proit is:(a) `9180 (b)`7150

(c) `3060 (d)`1440

(e)Noneof these

5. Four milkmen rented a pasture. A grazed 15 cowsfor 4 months, B grazed 12 cows for 2 months, Cgrazed18cowsfor6months,andDgrazed16cowsfor5months. IfA’sshareof rent is`1020, what is

C’s share of rent?

(a) `1836 (b)`1360(c) `816 (d)Cannot bedetermined

[OBC PO Examination, 2007]

6. Pankaj started abusiness investing`42000.After 4months Nitin joined himwith a capital of `57000.At the end of the year the total proitwas `26000.What is the difference between the share of proitsofPankaj andNitin?

(a) `1200 (b) `1400

(c) `1600 (d)`1800(e)Noneof these

[Corporation Bank PO Examination, 2007]

7. A started a business with `10000 and B joined him

later with a capital of `40000. If at the end of theyear, theybothgetanequal shareof theproit,howmanymonthsafterthebusinessstarteddidBjoinit?

(a) 4months (b)6months(c) 8months (d)9months

[SI of Police Rec. Examination, 1997]

8. A, B, C enter into a partnership investing `35000,

`45000 and `55000 respectively. The respectivesharesofA,B,Cinanannualproitof`40500 are:

(a) `13500, `16500,`10500

(b) `10500, `13500, `16500(c) `13500, `10500, `16600(d)Noneof these


25. A,BandCenteredintoapartnershipbyinvesting`12000, `15000 and `18000, respectively. A isalso a working partner and receiving 15% of theannual proit for his work. If B and C received

`8500 and`10200 from the annual proit as theirshares,whatamountdidAreceivefromtheannualproit?

(a) `10,500 (b) `11,500

(c) `11,300 (d) `14,000

1. A began business with `45000 and was joined

afterwards by B with `54000. After how manymonths, did B join if the proits at the end of theyear were divided in the ratio 2:1?

(a) 4 (b) 5

(c) 6 (d)7[SSC (GL) Prel. Examination, 2005]

2. Ninad, Vikas and Manav enter into a partnership.Ninad investssomeamountat thebeginning.Vikasinvestsdoubletheamountafter6monthsandManavinvests thrice theamount investedbyNinadafter8months.Theyearn aproitof`45000at the endoftheyear.What isManav’s share in theproit?(a) `25000 (b) `15000

(c) `12000 (d) `9000[SBI PO Examination, 2008]

3. Arun started a business investing `38000. After 5monthsBakul joinedhimwith a capital of`55000.At the end of the year the total proitwas `22000.Whatistheapproximatedifferencebetweentheshareof proits ofArun andBakul?(a) `1192 (b)`1856(c) `1007 (d) `1928(e) `1568

[IDBI Bank Examination, 2007]

4. Sarita startedabusiness investing`50000.After sixmonths, Abhishek joined her with `75000. AfteranothersixmonthsNishaalsojoinedthemwith`1.25lakh. Proit earned at the end of 2 yea`from whenSaritastartedthebusinessshouldbedistributedamongSarita,AbhishekandNishainwhatrespectiveratio?(a) 4:5:6 (b)8:9:10(c) 8:9:12 (d)4:5:8(e)Noneof these

[PNB Mgt. Trainee Examination, 2007]

ExErcisE-2 (BasEd on MEMory)

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Chapter 88.6

9. Three men rent a pasture for `660. The irst usesit to graze 50 sheep for 4months, the second usesit to graze 40 sheep for 3months and the third 46sheepfor5months.Howmuchshouldtheirstmanpay as rent?

(a) `276 (b)`220

(c) `144 (d) `240


10. A began business with `45000 and B joined

afterwards with `30000. At the end of a year, theproit is divided in the ratio 2:1.WhendidB join?(a) 3months after(b)6months after(c) 8months after(d)9months after

[Assistant’s Grade Examination, 1997]

11. A, B and C invested `10000, `14000 and

`12000, respectively in a business. If at the end ofa year, they got a proit of `5400, the share of Bin proit (if proit is divided in proportion to theinvestment of each) is:(a) `1500 (b) `2100

(c) `1800 (d)`150


12. A starts business with `3500 and after 5monthsBjoinswithA as his partner.After a year, the proitisdivided in the ratio2:3.What isB’scontributionin the capital?

(a) `8000 (b)`8500(c) `9000 (d)`7500

[SSC (GL) Prel. Examination, 2000]

13. A, B and C rent a pasture. A puts 10 oxen for 7months,Bputs12oxen for5monthsandCputs15oxenfor3monthsforgrazing. If therentof thepasture is `175, then how much C must pay as his

share of rent?(a) `45 (b) `50

(c) `55 (d) `60[SSC (GL) Prel. Examination, 2000]

14. A, B and C enters into a partnership their shares are

intheofratio1

2

1

3

1

4: : .After2months,Awithdraws

halfofhiscapitalAfter10months,aproitof`378is divided among them.What isB’s share?(a) `129 (b)`144

(c) `156 (d)`168[SSC (GL) Prel. Examination, 2000]

15. AandBarepartnersinabusiness.Acontrbutes 14

ofthecapitalfor15monthsandBreceived1

4ofthe

proit. Find for how long B’s money was investedin the business?

(a) 1 year (b)9months(c) 6months (d)10months


16. A, B and C are partners of a company. During aparticularyearAreceived1/3oftheproit,Breceived1

4

oftheproitandCreceivedtheremaining`5000.

How much did A receive?

(a) `5000 (b) `4000

(c) `3000 (d) `1000


17. A began a businesswith `4500. Later, B joinedAwith `5400. When did B join if the proits at theendof theyearweredivided in the ratio of 2:1?

(a) 4 months (b) 5 months

(c) 6months (d)7months[SSC (GL) Prel. Examination, 2000]

18. Vinay started a business investing `70000. Ashokjoined him after six months with an amount of`105000. Sunil joined them with `1.4 Lakh afteranother six months. The amount of proit earnedshould be distributed in what ratio among Vinay,AshokandSunil,threeyears afterVinaystartedthebusiness?

(a) 42:45:56 (b)7:6:10(c) 12:15:16 (d)Cannot bedetermined(e)Noneof these[PNB Management Trainee Examination, 2003]

19. Veena started a business, investing `75000. After3 months, Poonam joined her with an amount of`125000 and after another sixmonthsSarita joinedthem with an amount of `150000. Proit earned attheendof threeyears fromwhenVeenastartedthebusiness shoud be distributed in what ratio amongVeena,PoonamandSarita, respectively?

(a) 36:55:54 (b)18:28:27(c) 35:54:55 (d) Cannot be determined

(e)Noneof these[Bank of Maharashtra PO Examination, 2003]

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8.7Partnership

20. Three friendsX, Y and Z started a partnership fora period of 3 years by contributing capitals in theratioof5:4:2.WhatistheamountreceivedbyXashis share in the total proit?

I. Totalamountinvestedinthebusinessis`22000. II. Proitwasdistributed after a periodof 2 years. III.The average amount of proit earned per year

is `2750.(a) I only (b) II only

(c) III only (d) I or III only

[SBI PO Examination, 1999]

21. Three friends A, B and C started a business byinvestingcapitalsintheratios5:7:6.After6months,Cwithdrawshalfofhiscapital. If thesuminvestedby A is `40000, out of the total annual proit of`33000.C’s share will be:

(a) `9000 (b)`12000

(c) `11000 (d) `10000

[BSRB Hyderabad PO Examination, 1999]

22. MrSaxenastartedabusiness investing`5000.Fourmonthslater,MrJainjoinedthebusinessbyinvesting`9000.Iftheproitattheendoftheyearwas`22000,

then how much amount would Mr Jain have received

as theproit?(a) `16000 (b)`14000

(c) `12000 (d) `11000

[BSRB Delhi PO Examination, 2000]

23. Vinod and Ankit started a business by investingcapitalsintheratioof2:3.IfVinodhadinvestedanadditional amount of `10000, the ratio of Vinod’sinvestment to Ankit’s investment would have been3:2.Whatwas the amount investedbyVinod?(a) `8000 (b)`12000

(c) `9000 (d)Data inadequate[BSRB Patna PO Examination, 2001]

24. Vinay started a business investing `50000. After 1year, he invested another `30000 and Aditya also

joined him with a capital of `70000. If the proitearned in3years from the startingofbusinesswas`87500,indout the share ofAditya in theproit.(a) `37500 (b) `32500

(c) `38281 (d)Noneof these[Corporation Bank PO Examination, 2002]

25. A started a business with `10000.Bjoinedhimlaterwith a capital of `40000. If at the end of the year,they both received equal shares of the proit. HowmanymonthsafterthebusinessstarteddidBjoinit?

(a) 4months (b)6months(c) 8months (d)9months


26. A,B,C enters into a partnership investing`35000,

`45000 and `55000.The respectivesharesofA, B,

C in an annual proit of`40500 are:

(a) `13500, `16500,`10500

(b) `10500, `13500, `16500(c) `13500, `10500, `16600(d)Noneof these


27. Threemen rentapasture for`660.Theirstuses itto graze 50 sheeps for 4 months. The second usesittograze40sheepsfor3months.Thethirdusesitto graze46 sheep for 5months.Howmuch shouldtheirstmanpays as rent?(a) `276 (b)`220

(c) `144 (d) `240


28. A began a business with `45000. Later, B joinedhim with `30000.At the endof theyear, theproitwasdivided in the ratio of 2:1.WhendidB join?(a) 3months after (b)6months after(c) 8months after (d)9months after


29. A, B and C invested `10000, `14000 and `12000 in

a business. If at the end of a the business earns aproit of`5400, the share ofB in proit (if proit isdivided in proportion to the partner’s investments) is:

(a) `1500 (b) `2100

(c) `1800 (d)`150


30. A starts business with `3500.5monthslater B joins

A as his partner.After a year, the proit is dividedin the ratio of 2:3.What is B’s contribution in thecapital?

(a) `8000 (b)`8500(c) `9000 (d)`7500


31. Average score of Rahul,Manish and Suresh is 63.Rahul’s score is 15 less than Ajay and 10 more

thanManish.IfAjayscored30marksmorethantheaverage scores of Rahul,Manish and Suresh, whatis the sumofManish’s andSuresh’s scores?(a) 120 (b) 111

(c) 117 (d) Cannot be determined

[Corporation Bank PO Examination, 2011]

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Chapter 88.8

32. A and B enter into partnership with capitals in the

ratio 5:6. At the end of 8 months A withdrawshis capital. They received proits in the ratio 5:9.B invested the capital for:

(a) 6months (b)8months(c) 10 months (d) 12 months

[SSC, 2010]

33. A, B and C started a business investing `42000,

`30000 and `28000,respectively.After4months,Awithdrew `12000, B withdrew `6000andCwithdrew`8000. If, after 10months, a total proit of `46420is earned,what is the share ofC ?

(a) `12580 (b)`13160(c) `13020 (d) `12540

(e) `12760[IBPS PO/MT, 2014]

34. ThreemenA,BandCstartsabusinesstogether.Theyinvests `30000, `24000 and `42000, respectively, at

thebeginning.After4months,Bwithdrew`6000andC withdrew `10000.Theyreceivedaproitof`11960at the endof theyear.B’s share in theproit is:(a) `2700 (b) `2803(c) `2900 (d)`2785(e)Noneof these

[IBPS PO/MT, 2013]

35. An amount of money is to be divided among P,Q and R in the ratio of 3:5:7, respectively. If theamount received by R is `4,000 more than the amount

received by Q, what will be the total amount received

byP andQ together?(a) `8,000 (b)`12,000

(c) `16,000 (d)Cannot bedetermined(e)Noneof these

[Allahabad Bank PO, 2010]

ExErcisE-1

Explanatory answErs

answEr KEys

ExErcisE-1

1. (d) 2. (a) 3. (c) 4. (a) 5. (c) 6. (b) 7. (b) 8. (b) 9. (b) 10. (a) 11. (a) 12. (b) 13. (c)

14. (d) 15. (d) 16. (c) 17. (b) 18. (a) 19. (d) 20. (c) 21. (d) 22. (a) 23. (e) 24. (a) 25. (c)

ExErcisE-2

1. (d) 2. (b) 3. (b) 4. (b) 5. (a) 6. (e) 7. (a) 8. (b) 9. (d) 10. (d) 11. (b) 12. (c) 13. (a)

14. (b) 15. (d) 16. (b) 17. (d) 18. (c) 19. (a) 20. (c) 21. (a) 22. (c) 23. (a) 24. (d) 25. (d) 26. (b)

27. (d) 28. (d) 29. (b) 30. (c) 31. (b) 32. (d) 33. (e) 34. (b) 35. (c)

1. (d) Here, C1 = 50000, C2 = 40000 and P = 22500. ∴ C1 + C2 = 50000+ 40000= 90000.

∴Nikita’s share =C P

C C

1

1 2

50000 22500

90000

×+

=×

= 5

922500× = `12500.

2. (a) Ratio of the capitals = 75000:60000:40000= 15:12:8 ∴ Proit-sharing ratio = 15:12:8 Sumof the proit-sharing ratio = 15+ 12+ 8 = 35 Total proit = `26250

∴ Anu’s share = 8

35 × 26250

= `6000 3. (c) Here, C1 = 16000, C2 = 12000, C3 = 8000, t1 = 9,

t2 = 6, t3 = 12 and P = 26000. Suresh’s share in the proit

= C t P

C t C t C t

2 2

1 1 2 2 3 3

× ×+ +

= 12000 6 26000

16000 9 12000 6 8000 12

× ×× + × + ×

= 1872000000

312000

= `6000

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8.9Partnership

4. (a) Here,

C1 × t1 = 5000× 12+ 2000× 9 = 78000, C2 × t2 = 4000 × 1 + 3000 × 11 = 37000,

C3 × t3 = 7000 × 11 = 77000 and P = 1218. ∴ Rita’s share in the proit

= C t P

C t C t C t

3 3

1 1 2 2 3 3

× ×+ +

= 77000 1218

78000 37000 77000

×+ +

= `488.47.

5. (c) We have, C1 × t1 = 3500 × 12 = 42000

and C2 × t2 = x × 7 = 7x.

Then, Profit for A

Profit for B=

×

×

C t

C t

1 1

2 2

⇒ 2

3

42000

7=

x or x =

42000 3

2 7

×

× = `9000.

6. (b) Let,Bansal’s capital be invested for xmonths.

Then, we have 5 8

6

5

9

××

=

x

⇒ x = 5 8 9

6 5

× ×

×

= 1month.

∴Bansal’s capitalwas invested for 12months. 7. (b) Let,Brij remain in the business for xmonths. We have, C1 × t1 = 550× 12= 6600 C2 × t2 = 330 × x = 330x

∴

Arvind s share of profit

Brij s share of profit

C1�

�=

×

×

t

C t

1

2 2’

’

⇒ 10

3

6600

330

6600 3

330 10= ⇒ =

×

×xx = 6months.

8. (b) Let, B remain in the business for x months. We have, C1 × t1 = 3750 × 12 = 45000

and C2 × t2 = 5000 × x = 5000 x

∴ A�s share in profit

B�s share in profit=

×

×

C t

C t

1 1

2 2

’

’

⇒ 1

1

45000

5000=

x

or, x = 45000

5000= 9months

9. (b) Let,Brijesh’s capital be invested for xmonths. Capital ratio ofAnju andBrijesh is 5:9. Let the capitals ofAnju andBrijesh be `5y and `9y. We have, C1 × t1 = 5y × 8 = 40y

and, C2 × t2 = 9y × x = 9yx

∴ Anju s share of profit

Brijesh s share of profit

C1�

�=

×

×

t

C t

1

2 2

⇒ 4

9

40

9=

y

yx ⇒ x =

40 9

4 9

×

×

= 10months.

’

’

10. (a) Ratio of capitals of A, B and C is 3:5:9. Let thecapitals ofA,B andC be 3x, 5x and 9x, respectively.

Ratiooftimingoftheirinvestmentsare2:3:1.Let,A,BandCinvesttheircapitalsfor2y, 3y and ymonths,respectively.

Then, proit ofA : proit ofB : proit ofC = C1 × t1:C2 × t2:C3 × t3 = 3x × 2y:5x × 3y:9x × y

= 6:15:9 or 2:5:3. 11. (a) We have, C1:C2:C3 = 1:2:3

and P1:P2:P3 = 1:2:3.

∴ Required ratio = P

C

P

C

P

C

1

1

2

2

3

3

1

1

2

2

3

3: : : :=

or, 1:1:1. Thus,Sumit,PunitandRamit invested theircapitals for

equal period of time. 12. (b) We have, P1:P2:P3 = 4:5:6 and t1:t2:t3 = 2:3:6.

∴ Required ratio = P

t

P

t

P

t

1

1

2

2

3

3

4

2

5

3

6

6: : : :=

or, 12:10:6. Thus, A, B and C invested their capitals in the ratio of

12:10:6. 13. (c) Ratio in which A, B, C pays the rent

= (6 × 12):(8 × 7):(6 × 8) = 72:56:48 = 9:7:6

Rent paid by A = 9

22396× ` = `162.

14. (d) D’s capital = 1 − − − =

1

3

1

4

1

5

13

60

Proit ratio ofA,B,C,D=13

1

4

1

5

13

60: : :

⇒ 20:15:12:13

∴ Share ofD=1360

6000× ` = `1300.

15. (d) Obviously,C invests for 12 – 4 = 8months. ∴ Equivalent capitals are

`1500× 1; `2000 × 9

12 = `1500,

`2250 × 8

12 = `1500

∴ Proit is to be shared in the ratio of 1500:1500:1500= 1:1:1. 16. (c) Let,investmentsofAandBbe5x and 7x. The period

ofB’s investment be for y months

Then, ( )

( )

5 7

7

1

2

x

x y

××

= ⇒ y = 10.

17. (b) Total proit in a business = `1040

Separate proit forA= 25%of `1040

= 1040 25

100

× = `260

Remaining proit = `(1040 – 260) = `780

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Chapter 88.10

The remaining proit will be divided in proportion totheir capitals.

∴RatiobetweencapitalsofAandB=2100:3100=21:31 SumofEditor : proportional? capital? = 21+ 31= 52

∴ A’s proit = 2152

780× = `315

B’s proit = 3152

780× = `465

Total proit ofA= `(315+ 260) = `575

Therefore,AandB’sproitshareswillbe`575 and `465.

18. (a) Suppose, total proit in the business = `x

∴ 60%of total proit = 60%of x = `3

5

x

∴Thetwopartnerswillreceiveproitof` 310

x and `

3

10

x,

respectively.

∴Remaining proit = x – 35

x = `

2

5

x .

The remaining proit assumed as interest on the capitalwill be divided in the proportion of their capitals.

Their capital ratio = 12500:8500= 25:17 Sumof proportionals = 25+ 17= 42

∴The irst partner’s proit =25

42

2

5

5

21× =

x x`

The second partner’s proit = 1742

2

5

17

105× =

x x`

Given 3

10

5

21

3

10

17

105

x x x x+ = + + 300

∴ 8

105

x = 300

or, x = 105 300

8

× = `3937.50

∴Total proit in the business = `3937.50.

19. (d) The given ratio = 72

4

3

6

5: : = 105:40:36

Let they initially invest `105, `40 and `36,respectively. Ratio of investments = [105× 4 + (150%of 105) × 8]:(40× 12):(36× 12) = 1680:480:432= 35:10:9

B’s share = ` 2160010

54×

= `4000.

20. (c) Let the total proit be `100.

After paying the charity,A’s share = ` 953

5×

= `57

IfA’s share is `57, total proit = `100

IfA’s share is `855, total proit = ` 855100

57×

= `1500.

21. (d) A’s share formanaging the business

= 121

2% of `880= `110

Remaining proit = `770

Proit ratio ofA andB= 5:6

A’s share = 5

11 of `770 = `350

A’s total proit = `350 + `110 = `460.

22. (a) Proit ratio ofA,B andC is

(1200 × 12):(x × 9):(y × 6) = 2:3:5

⇒ 1200 12

2

9

3

×=

x

∴ x = `2400.

23. (e) Share ofC in proit =C t P

C t C t C t

3 3

1 1 2 2 3 3

×+ +

[Here, C1 × t1 = 3512420 × 2 + 2412420 × 1

C2 × t2 = 4222180× 3’C3 × t3

= 4065400× 2 + 4865400× 1 andP = 105300]

=

( )

( )

4065400 2 4865400 1

1053000

3512420 2 2412420 1 4222180

× + ××

× + × + ××+ × + ×

3

4065400 2 4865400 1( )

= `389886.

24. (a) Let the total proit be `x

Salary given toB= `1440

∴Net proit = x – 1440

∴ Share ofA andB each=x −1440

2

Interest given byB toA= 10100

22500× = `2250.

∴

x

x

−+ −

−+

=

1440

21440 2250

1440

22250

1

2

or, x

x

−

+=

3060

3060

1

2

∴ x = `9180.

25. (c) CapitalratioofA,B,Cis12000:15000:18000=4:5:6

Proit ratio ofB andC= 8500:10200= 5:6

∴A’s share of proit =4

58500× Rs. = `6800

85%of x = 6800+ 8500+ 10200

= 25500

∴ 15%of x = 25500 15

85

× = 4500

Total proit ofA= `6800+ `4500 = `11300.

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8.11Partnership

ExErcisE-2 (BasEd on MEMory)

1. (d) SupposeB joined after x months

∴ 45000 12

54000 12

2

1

×

× −( )=

x

⇒ 45000 × 12

= 54000× 12× 2 – 54000× 2 × x ⇒ 108x = 54× 24 – 45× 12 ⇒ 27x = 54× 6 – 45× 3 ⇒ 27x = 324 – 135= 189 ⇒ x = 7

∴ B joined after 7months.

2. (b) Let the investment ofNinad be `x

∴ Investment ofVikas = `2x

and investment ofManav= `3x

∴ Ratio of their investments = x × 12:2x × 6:3x × 4

= 12x:12x:12x = 1:1:1

∴ Manav’s share in the proit

= 1

345000× = `15000

3. (b) Ratio of investment is:Arun:Bakul = 38000× 12:55000× 7 = 38 × 12:55× 7 = 456:385≈ 45:38

Required difference = 2200045 38

45 38+

× −( )

=×

≈ ≈ ≈22000 7

83

22000

121835 1856`

4. (b) Sarita:Abhihek:Nisha = 50000× 24:75000× 18:125000× 12 = 2 × 24:3 × 18:5 × 12 = 2 × 4:3 × 3:5 × 2 = 8:9:10 5. (a) 15 × 4 = `1020

∴ 18 61020

15 418 6 1836× ≡

×

× =( ) `

6. (e) Ratio of their shares = 42× 12:57× 8 = 14× 12:19× 8 = 21:19 Required difference in shares

=

+

× − =26000

21 1921 19 1300( ) `

7. (d) Suppose, B joinsA afterKmonths. ∴ Investments ofA andB are in the ratio of 10000× 12:40000× (12 –K)

∴ 10000× 12= 40000× (12 –K)

i.e., 4(12 –K) = 12 ⇒ K = 9.

8. (b) A, B, C invest in the ratio

35000:45000:55000 i.e., 7:9:11

∴ A’s share in the proit = 727

40500×

= 7 × 1500 = `10500

B’s share in the proit = 9 × 1500= `13500

C’s share in the proit = 11× 1500= `16500.

9. (d) They pay in the ratio 50× 4:40× 3:46× 5 i.e., 200:120:230 i.e., 20:12:23

∴ 1st man should pay `20

55660× = `240.

10. (d) SupposeB joined afterK months

∴ Proit is divided in the ratio of 45000 × 12:30000 × K

∴ 45000 12

30000

2

1

×

×

=

K ⇒ 60000K = 540000

∴ K = 9.

11. (b) Proit is divided between A, B and C in the ratio10:14:12

i.e., 5:7:6

∴ B’s share = 7

185400× = `2100.

12. (c) Let B’s contribution be `x

∴ 3500 12

7

2

3

×=

x

or, x = 3500 12 3

7 2

× ×× ∴ x = 9000.

13. (a) A,B andC pay in the ratio of 10 × 7:12 × 5:15 × 3

i.e., 70:60:45 i.e., 14:12:9

∴ C pay `9

35 × 175 = `45.

14. (b) Suppose, shares ofA,B andC are 6K, 4K and 3K,

respectively. ∴Proitof378isdividedamongthemintheratioof6K

× 2 + 3K × 10:4K × 12:3K × 12

i.e., 42:48:36 i.e., 7:8:6

∴ B’s share = 8

21378× = `144.

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Chapter 88.12

15. (d) A’s capital = 1

4K

B’s capital = 3

4K

A and B share the total proit in the ratio 1:2. Let Bcontribute for x months

∴

1

415

3

4

1

2

K

K x

×

×

= ⇒ x = 10.

16. (b) Proit earned by

C = 11

3

1

41

7

12

5

12− +

= − =

So, 5

12 = 5000 ∴ 1→12000

∴ Proit received byA = 1

312000× = `4000.

17. (d) Suppose,B joined afterK months

∴ 4500× 12:5400× (12 –K) = 2:1

⇒ 4500 12

5400 12

2

1

×

× −=

( )K

⇒ 60

6 12

2

1( )−

=

K

⇒ 12(12 –K) = 60⇒ K = 7.

18. (c) Ratio of their investments = 70× 36:105× 30:140× 24 = 12:15:16.

19. (a) Ratio of their proits = 75× 36:125× 33:150× 27 = 3 × 36:5 × 33:6 × 27 = 3 × 12:5 × 11:6 × 9 = 36:55:54.

20. (c) Wheninvestmentratioisgiven,theamountofproitcan be found outwith the help of III only.

21. (a) Sum invested by A, B and C is

5 × 12:7 × 12:6 × 6 + 3 × 6 or, 60:84:54 or, 10:14:9

∴ Share ofC=9

3300033

× = `9000.

22. (c) Ratio of their investments = 50000× 12:90000× 8 = 5:6 ∴ Amount received by Mr Jain

= 6

2200011

× = `12000.

23. (a) LettheinitialinvestmentsofVinodandAnkitbe2x

and 3x, respectively. As per the question,

2 10000

= 3

2

or, 4x + 20000= 9x

∴ x = 4000

∴ Amount invested byVinod = 2x = `8000. 24. (d) Ratio ofVinay andAditya for onemonth = (50000× 12) + (80000× 24):(70000× 24) = 60000+ 1920000:1680000= 3:2 Hence, share of Aditya in the proit earned from the

business = 87,500

23 2

×+

= `35000.

25. (d) Suppose, B joinsA afterKmonths. ∴ Investments ofA andB are in the ratio of 10000× 12:40000× (12−K)

∴ 10000× 12= 40000× (12−K)

That is, 4 (12−K) = 12 ⇒ K = 9. 26. (b) A, B, C invest in the ratio 35000:45000:55000

That is, 7:9:11

∴ A’s share in the proit =7

4050027

×

= 7 × 1500 = `10500

B’s share in the proit = 9 × 1500= `13500

C’s share in the proit= 11× 1500= `16500. 27. (d) They pays in the ratio of 50× 4:40× 3:46× 5 That is, 200:120:230

That is, 20:12:23

∴ The irstman should pay ` 20660

55× = `240.

28. (d) Suppose,B joined afterK months

∴ Proit is divided in the ratio of 45000 × 12:30000 × K

∴ 45000 12

30000 K

××

= 2

1

⇒ 60000K = 540000

∴ K = 9.

29. (b) Proit is divided amongA, B and C in the ratio of 10:14:12.

That is, 5:7:6

∴ B’s share = 7

540018

× = `2100.

30. (c) Let, B’s contribution be `x

∴ 3500 12

7x

× =

2

3

or, x = 3500 12 3

7 2

× ××

∴ x = 9000.

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8.13Partnership

31. (b) Let the score ofAjay= x Rahul = x − 15 Manish = x − 25 As per the question, x = 63+ 30 ∴ x = 93 ∴ Score ofAjay= 93 then, Rahul = 93− 15= 78 then, Manish = 93− 25= 68 Totalmarks ofRahul,Manish andSuresh = 3 × 63= 189 ∴ Suresh= 189− (78+ 68) = 43 ∴ Manish + Suresh= 68+ 43= 111

32. (d) Let A’s amount be 5x

B’s amount be 6x

Again, letB invested the capital for y months

Now, according to the question,

5 8

6

5

9

x

x y

××

=

⇒ 40

6

5

9y=

∴ y =×

×

=9 40

6 512 months

33. (e) Ratio of proits amongA,B andC = (42000 × 4 + 30000 × 6):(30000× 4 + 24000 ×

6):(28000×4 + 20000 ×6) =(168000+180000):(120000+ 144000):(112000 + 120000)

= 348000:264000:232000 = 348:264:232

Hence, C’s share = × =46420

844232 12760`

34. (b) Ratio of capital =(30000×12):(24000×4+18000×8) : (42000×4+

32000× 8) = 36000:(96000+ 144000):(168000+ 256000)

= 360000:240000:424000

= 360:240:424= 45:30:53 Sumof ratios = 45 + 30+ 53= 128

Now,B’ share = × = ≈30

12811960 2803 125 2803` `.

35. (c) DifferenceofamountreceivedbyR and Qis(7−5)= 2, Total amount received by P and Q = (3 + 5) = 8.

Then, 2 corresponds to `4000impliesthat8corresponds

to 4000

28 16000× = ` .

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