Partnership problems
- 1. A and B invest in a business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share is Rs. 855, the total profit is :
Options- A. 500
- B. 1000
- C. 1500
- D. 2000 Discuss
Correct Answer: 1500
Explanation:
Let the total profit be Rs. 100.
After paying to charity, A's share = (95*3/5) = Rs. 57.
If A's share is Rs. 57, total profit = Rs. 100.
If A's share is Rs. 855, total profit = (100/57*855) = 1500.
- 2. A, B, C started a business with their investments 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 investments. The ratio of their profits at the end of the year is :
Options- A. 1 : 2 : 3
- B. 3 : 4 : 15
- C. 3 : 5 : 10
- D. 5 : 6 : 10 Discuss
Correct Answer: 5 : 6 : 10
Explanation:
Let their initial investments be x, 3x and 5x respectively. Then,
A:B:C = (x*4+2x*8) : (3x*4+(3x/2)*8) : (5x*4+(5x/2)*8)
20x : 24x : 40x = 5 : 6 : 10
- 3. 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 withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?
Options- A. 144
- B. 169
- C. 225
- D. 339 Discuss
Correct Answer: 144
Explanation:
Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
B's share = Rs. (378 * 8/21) = Rs. 144.
- 4. A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used ?
Options- A. 3 months
- B. 6 months
- C. 10 months
- D. 12 months Discuss
Correct Answer: 10 months
Explanation:
Let the total profit be Rs. z. Then,
B's share = Rs. 2z/3, A's share = Rs. ( z - 2z/3 ) = Rs. z/3.
A : B = z/3 : 2z/3 = 1:2
Let the total capital be Rs, X and suppose B's money was used for x months. Then.
(1(x) / 4 * 15) / (3x) / 4 * y) = 1/2 <=> y = (15 * 2 / 3) = 10 .
Thus, B's money was used for 10 months.
- 5. A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?
Options- A. 4 months
- B. 5 months
- C. 6 months
- D. 8 months Discuss
Correct Answer: 8 months
Explanation:
Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3) = 8.
So, B joined for 8 months.
- 6. If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 4650, C will receive ____
Options- A. Rs.700
- B. Rs.800
- C. Rs.900
- D. Rs.1000 Discuss
Correct Answer: Rs.900
Explanation:
Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .
A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.
Hence, C's share (4650 * 6/31) = Rs, 900.
- 7. A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
Options- A. Rs. 45
- B. Rs. 50
- C. Rs. 55
- D. Rs. 60 Discuss
Correct Answer: Rs. 45
Explanation:
A:B:C = (10×7):(12×5):(15×3)
= 70 :60 :45
= 14 :12 :9
C's rent = Rs.(175×9/35)
=Rs. 45.
- 8. Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is :
Options- A. 8400
- B. 8200
- C. 8100
- D. 8000 Discuss
Correct Answer: 8400
Explanation:
Ratio of their shares = 22500 : 35000 = 9 : 14.
Deepak's share = Rs. (13800 * 14/23) = Rs. 8400.
- 9. A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
Options- A. Rs. 39000
- B. Rs. 49000
- C. Rs. 59000
- D. Rs. 69000 Discuss
Correct Answer: Rs. 59000
Explanation:
Interest received by A from B = 10% of half of Rs.50000 = 10% of Rs. 25000 = Rs.2500.
Amount received by A per annum for being a working partner = 1500 x 12 = Rs.18000
Let 'P' be the part of the remaining profit that A receives as his share.
So,total income of A = (Rs.2500 + Rs.18000 + Rs. P )
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
We know that income of A = Twice the income of B
So, (2500 + 18000 + P ) = 2(P)
P = 20500
Thus, the total profit = 2P + Rs.18000
= 2(20500) + 18000 = Rs.59000.
- 10. A, B and C enter into a partnership with a capital in which A's contribution is Rs. 10,000. If out of a total profit of Rs. 1000, A gets Rs. 500 and B gets Rs. 300, then C's capital is :
Options- A. 4000
- B. 5000
- C. 6000
- D. 7000 Discuss
Correct Answer: 4000
Explanation:
A : B : C = 500 : 300 : 200 = 5 : 3 : 2.
Let their capitals be 5x, 3x and 2x respectively.
Then, 5x = 10000
=> x = 2000.
C's capital = 2x = Rs. 4000.
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