Question

X, Y, and Z started a business with capitals in the ratio 2:3:5. After 3 months, Z withdrew 40% of his capital. After another 3 months, Y withdrew half of his capital. The business continued for a total of 18 months. If total profit is ₹3,24,000, find the ratio of profit shares of X:Y: Z.

• A. 3 : 3 : 5
• B. 3 : 3 : 4
• C. 1 : 2 : 2
• D. 1 : 3 : 1

Answer 1

Answer:

A. 3 : 3 : 5

Let the initial capitals of X, Y, and Z be:

2k : 3k : 5k

Profit is shared according to Capital × Time.

X's contribution

X keeps his capital for all 18 months:

$2k \times 18 = 36k$

Y's contribution

• First 6 months: (3k)

• Then withdraws half, leaving (1.5k) for the remaining 12 months

$3k \times 6 + 1.5k \times 12$
= 18k + 18k
= 36k

Z's contribution

• First 3 months: (5k)

• Withdraws 40%, so remaining capital = (60%) of (5k = 3k)

• Remaining 15 months: (3k)

$5k \times 3 + 3k \times 15$
= 15k + 45k
= 60k

Profit-sharing ratio

X:Y:Z = 36:36:60 = 3:3:5
Ratio of profit shares =$(\boxed{3:3:5})$