# Partnerships Quiz Set 004

### Question 1

P and Q start a business with investments in the ratio 5 : 14. After 3 months, P increases his capital by \$1/5\$th, and Q increases his capital by \$1/14\$th. If the profit at the end of 10 months is 816, then what is the share of P?

A

Rs. 228.

B

Rs. 328.

C

Rs. 128.

D

Rs. 428.

Soln.
Ans: a

After 3 months, the ratio of their capitals is 6:15. The ratio of money-months of P and Q is \${5 × 3 + 6 × 7}/{14 × 3 + 15 × 7}\$, which is \$57/147\$. Profit of P = \$57/{57 + 147}\$ × 816 = Rs. 228.

### Question 2

X starts a business with a capital of Rs. 1800. Some months later Y joins him with a capital of Rs. 900. For how much period does Y join if the profits are shared in the ratio 4 : 1?

A

6.

B

7.

C

5.

D

8.

Soln.
Ans: a

Money-months of X are 1800 × 12 = 21600. If money-months of X are 4 then money-months of Y are 1. So, if money-months of X are 21600, money-months of Y are \$1/4 × 21600\$, which gives months of Y = \${1 × 21600}/{4 × 900}\$ = 6 months.

### Question 3

X starts a business with a capital of Rs. 3200. Some months later Y joins him with a capital of Rs. 400. For how much period does Y join if the profits are shared in the ratio 16 : 1?

A

6.

B

7.

C

5.

D

8.

Soln.
Ans: a

Money-months of X are 3200 × 12 = 38400. If money-months of X are 16 then money-months of Y are 1. So, if money-months of X are 38400, money-months of Y are \$1/16 × 38400\$, which gives months of Y = \${1 × 38400}/{16 × 400}\$ = 6 months.

### Question 4

A, B and C hire a coffee vending machine. A uses it for 3 hours and prepares 15 cups, B uses it for 4 hours and prepares 4 cups and C uses it for 16 hours and prepares 6 cups. If the total rent is Rs. 628, how much should A pay?

A

Rs. 180.

B

Rs. 190.

C

Rs. 170.

D

Rs. 200.

Soln.
Ans: a

Sum of the cup-hours is 15 × 3 + 4 × 4 + 16 × 6 = 157. Share of A = \${15 × 3}/157\$ × 628 = Rs. 180.

### Question 5

A, B and C start a partnership business. A invests Rs. 400 and C invests Rs. 500. What should B have invested if it wanted to earn a share of Rs. 250 in the annual profit of Rs. 500?

A

Rs. 450.

B

Rs. 550.

C

Rs. 350.

D

Rs. 650.

Soln.
Ans: a

By inspection, the desired share is 1/2 of the annual profit. So B should have contributed half of the capital, which is \${400 + 500}/2\$ = Rs. 450. 