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SOLVED EXAMPLES

Example 1 :
A starts a business by investing Rs. 500. B joins him after two months by investing Rs. 400 and C joins them after 6 months by investing Rs. 800. If the annual profit is Rs. 444. Find the profit of C.
(1) 180      (2) 120      (3) 144      (4) 148      (5) 146
Sol. 3 (144)
Explanation:
A investing = 500 × 12 = 6000
B’s investment = 400 × 10 = 4000
C’s investment = 800 × 6 = 4800
Their ratio = 6000 : 4000 : 4800 = 15 : 10 : 12

 

Example 2 :
A, B, C go into business as partners and collect a profit of Rs. 1000. If A’s cpaital : B’s capital = 2 : 3 and B’s capital : C’s capital = 2 : 5. Find the share of profit which goes of C.
(1) 160      (2) 240      (3) 500    (4) 600      (5) 750
Sol. 4(600)
Explanation:
A’s Capital : B’s Capital = 2 : 3
B’s Capital : C’s Capital = 2 : 5
A’s Capital : B’s Capital : C’s Capital

 

Example 3 :
A, B and C are partners of a company during the particular year, A received of profit B received of the profit and C received remaining Rs. 5000. How much did A received?
(1) Rs.5000         (2) Rs.4000       (3) Rs.3000     (4) Rs.1000     (5) Rs.4500
Sol. 2(Rs.4000)
Explanation:

 

Example 4 :
P and Q entered into partnership with Rs. 700 and Rs. 600 respectively. After 3 months P withdraw of his 2/7 stock but after 3 months more he put back 3/5  of what he had withdrawn. The profits at the end of the year are Rs. 726. How much of this should P receive ?
(1) Rs.633         (2) Rs.336      (3) Rs.663      (4) Rs.366      (5) Rs.363
Sol. 4(Rs.366)
Explanation:
Ratio of their invests

⇒ 2100 + 500 × 3 + 620 × 6 : 7200
⇒ 2100 + 1500 + 3720 : 7200
⇒ 7320 : 7200   61 : 60

 

Example 5 :
A started a business by investing Rs. 2700. After sometime B joined him by investing Rs. 2025. At the end of one year, the profit was divided in the ratio 2 : 1 after how many months did B join the business?
(1) 4 months      (2) 6 months     (3) 3 months      (4) 2 months      (5) 5 months
Sol. 1 (4 months)
Explanation:
Let ‘B’ invest time = x month after
2700 × 12 : 2025 × (12 – x) = 2 : 1
⇒ 2700 × 12 = 2025 (12 – x) ⇒ x = 4

 EXERCISE

 

1. A and B rent a pasture for 12 months. A puts in 350 oxen for 5 months. How many can B put in for the remaining 7 months if he pays as much against A?
(1) 350     (2) 300        (3) 530      (4) 400     (5) 380
Ans: 350
Explanation:

 

2. Three men P, Q and R start business together. They invest Rs. 30000, Rs. 24000 and Rs. 42000, respectively in the beginning. After 4 months, Q took out Rs. 6000 and R took out of Rs. 10000. They get a profit of Rs. 11960 at the end of the year. Q’s share in the profit? (approx.)
(1) Rs.2803    (2) Rs.2748    (3) Rs.2930    (4) Rs.2785     (5) Rs.2083
Ans: Rs.2803   
Explanation:
P, Q, R partnership in the ratio
P : Q : R = 30000 : 24000 : 42000
New shares of P, Q, R, for 1 yr. in the partnership,
Share of P = 30000 × 12 = 360000
Share of Q = 24000 × 4 + (24000 – 6000) × 8 = 240000
Share of R = 42000 × 4 + (42000 – 10000) × 8 = 424000
P : Q : R = 360000 : 240000 : 424000  = 360 : 240 : 424 = 45 : 30 : 53
Q’s share in the profit

 

3. A, B and C started a shop by investing Rs. 27000, Rs. 81000 and Rs. 72000 respectively. At the end of one year B’s share in total profit was Rs. 36000/ What was the total profit.
(1) Rs. 116000        (2) Rs. 80000        (3)Rs.  100000        (4) Rs. 95000        (5) Rs. 90000
Ans: Rs. 80000
Explanation:

 

4. A, B and C were sharing profits in the ratio 4 : 3 : 2. B retired from the firm and A and C decided to share profits in the ratio 3 : 2. Calculate the gaining ratio?
(1) 7 : 8        (2) 9 : 5        (3) 4 : 7        (4) 5 : 8        (5) 8 : 7
Ans: 350
Explanation:

 

5. Rajiv, Raghu and Rohan enter into a partnership. Rajiv invests some amount at the beginning. Raghu invests double the amount after six months and Rohan invests thrice the amount invested by Rajiv after 8 months. They earn a profit of Rs. 45000 at the end of the year. What is Rohan’s shar in the profit.
(1) 20000      (2) 12000     (3) 15000     (4) 10000    (5) 18000
Ans:  15000
Explanation:
Rajiv invest = Rs. x
Raghu invest = Rs. 2x
Rohan invest = Rs. 3x
Their ratio of the equivalent capitals  = 12 × x : 6 × 2x : 4 × 3x = 1 : 1 : 1

 

6. Deepthi invested an amount of Rs. 60000 to start of software business. After 6 months, Divya joined her with an amount of Rs. 90000. After one year from the start of the business, Deepthi put in an additional amount of Rs. 20000. At the end of 3 years, they earned a profit of Rs. 712000. What is Deepthi’s share in the profit.
(1) 264000        (2) 352000     (3) 384000    (4) 270000     (5) 325000
Ans:  352000
Explanation:
Their ratio = (60000 × 1 + 80000 × 2) : 90000 × 2½
= 220000 : 225000 = 44 : 45
Sum of the ratio = 44 + 45 = 89
Total profit = Rs. 712000

 

7. A, B and C started a business with their investment in the ratio 1 : 3 : 5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investment. The ratio of their profits at the end of the year was
(1) 5 : 6 : 10       (2) 6 : 5 : 10     (3) 10 : 5 : 6    (4) 4 : 3 : 5    (5) 10 : 6 : 5
Ans: 5 : 6 : 10  
Explanation:

 

8. A, B and C invested their capitals in the ratio of 5 : 6 : 8 at the end of the business. They received the profits in the ratio of 5 : 3 : 1. Find the ratio of time of which they contributed their capitals.
(1) 12 : 9 : 7 (2) 8 : 4 : 1  (3) 25 : 8 : 18 (4) 7 : 6 : 5 (5) 4 : 8 : 1
Ans: 8 : 4 : 1
Explanation:

 

9. Two Friends P and Q started a business investing in the ratio of 5 : 6. R joined them after 6 months investing an amount equal to that of Q’s. At the end of the year, 20% of profit was earned which was equal to Rs. 98,000. What was the amount invested by R?
(1) 105000    (2) 175000    (3) 210000    (4) 222000    (5) 100500
Ans: 105000
Explanation:
Let the total investment Rs. x
Then 20% of x = 98000

Let the capitals P, Q, R be Rs. 5x, 6x, 6x respectively.
∴ 5x × 12 + 6x × 12 + 6x × 6 = 490000
⇒ 168x = 490000 ⇒ x = 2916.66
R’s investment = 6x × 6 = 36 × 2916.66 = 105000

 

10. A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months. B, Rs. 8400 for 5 months and C, Rs. 10000 for 3 months. A wants to be the working member for which he has to receive 5% of the profit. The profit earned was Rs. 7400. Calculate the share of B in the profit.
(1) 2660       (2) 2840     (3) 2800        (4) 1900    (5) 2600
Ans: 2660
Explanation:
A receive profit = 5% of 7400 = 370
Remaining profit = 7400 – 370 = 7030
Ratio of their investments
= 6500 × 6 : 8400 × 5 : 10000 × 3 = 13 : 14 : 10

11. A, B and C enter into a partnership and their shares are in the ratio 1/2:1/3: 1/4  after 2 months A withdraw half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B’s share?
(1) 129       (2) 144    (3) 156   (4) 168     (5) 196
Ans: 144
Explanation:

 

12. Two partners invest Rs. 6280 and Rs. 3768 respectively in a business and agree that 30% profit should be divided equally between them and the remaining profit is to be treated as interest on capital. If one partner gets 700 more than other. Find the total profit made by the business.
(1) 4000        (2) 3800       (3) 4125        (4) 4500       (5) 4100
Ans: 4000
Explanation:
Quicker method :
Applying the above rule we have
Step I :
The ratio of profit = 6280 : 3768 = 785 : 471
Step II :

 

13. A and B invested in the ratio 4 : 9 in a business. If 8% of the total profit goes to charity and A’s share is Rs. 460. Find the total profit.
(1) 2625           (2) 2526            (3) 1526            (4) 1625 (5)            1650
Ans: 1625
Explanation:

 

14. A puts Rs. 768 more in a business than B, but B has invested his capital for 7 months while A has invested his for 4 months. If the share of A is Rs. 42 more than that of B out of the total profits of Rs. 358, find the capital contributed by B?
(1) Rs. 642         (2) Rs. 1400     (3) Rs. 632       (4) Rs. 462     (5) Rs. 623
Ans:  Rs. 632      
Explanation:
Let the investment of B = x
A’s investment = x + 768
From question,
A’s share = 42 + B’s share ...(1)
Actual (A + B)’s share = 358 ...(2)
From (1) and (2)
A’s share = 200, B’s share = 158
∴ (x + 768) 4 = x × 7 = 200 : 158
⇒ (x + 768) 4 × 158 = 7x × 200
⇒ 158x + 158 × 768 = 350x
⇒ 192x = 768 × 158 ⇒ x = Rs. 632.
∴ B’s Capital = Rs. 632.

 

15. Rahul and Raju start a business with investment of Rs. 2500 and Rs. 2250 respectively. After 2 months, Rahul takes out Rs. 1250 from his capital. After one month, Raju takes out Rs. 750 of his capital while Ramesh joins them with a capital of Rs. 3500. At the end of 6 months, they earn a profit of Rs. 2540. Which of the following is the share of Rahul ?
(1) 800       (2) 900      (3) 840    (4) 900     (5) 700
Ans: 800
Explanation:
Rahul investment = 2500
After 2 months he withdraw Rs. 1250 from capital.
∴ Rahul invested for Rs. 2500, 2 months and (2500 – 1250) = 1250 for 4 months.
Raju = (2250 – 750) = 1500 for 3 months
Their ratio
= (2500 × 2 + 1250 × 4) : (2250 × 3 + 1500 × 3) : 3500 × 3
= 10000 : 11250 : 10500 = 40 : 45 : 42.
Total profit for 6 months = Rs. 2540

Posted Date : 10-02-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్లో వచ్చే ప్రకటనలు అనేక దేశాల నుండి, వ్యాపారస్తులు లేదా వ్యక్తుల నుండి వివిధ పద్ధతులలో సేకరించబడతాయి. ఆయా ప్రకటనకర్తల ఉత్పత్తులు లేదా సేవల గురించి ఈనాడు యాజమాన్యానికీ, ఉద్యోగస్తులకూ ఎటువంటి అవగాహనా ఉండదు. కొన్ని ప్రకటనలు పాఠకుల అభిరుచిననుసరించి కృత్రిమ మేధస్సు సాంకేతికతతో పంపబడతాయి. ఏ ప్రకటనని అయినా పాఠకులు తగినంత జాగ్రత్త వహించి, ఉత్పత్తులు లేదా సేవల గురించి తగిన విచారణ చేసి, తగిన జాగ్రత్తలు తీసుకొని కొనుగోలు చేయాలి. ఉత్పత్తులు / సేవలపై ఈనాడు యాజమాన్యానికి ఎటువంటి నియంత్రణ ఉండదు. కనుక ఉత్పత్తులు లేదా సేవల నాణ్యత లేదా లోపాల విషయంలో ఈనాడు యాజమాన్యం ఎటువంటి బాధ్యత వహించదు. ఈ విషయంలో ఎటువంటి ఉత్తర ప్రత్యుత్తరాలకీ తావు లేదు. ఫిర్యాదులు తీసుకోబడవు.

 

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