Question

In a partnership business, A’s capital was 1/3^rd more than B’s capital. After 5 months A withdrew 50% of his capital and after 3 more months B withdrew 1/3^rd of his capital. Then the profit ratio of A and B after one year will be?
1. 16 : 17
2. 35 : 34
3. 17 : 18
4. 17 : 16

Answer 1

Correct Answer - Option 4 : 17 : 16

A’s capital = B’s capital + 1/3^rd of B’s capital = 4/3 × B’s capital

Time period of A for 100% capital = 5 months and remaining 50% = 7 months, (50% withdrew)

Time period of B for 100% capital = 8 months and remaining 66.66% = 4 months, (1/3^rd withdrew)

Concept used:

Ratio of product of time and investment = Ratio of profit

Calculation:

Let B’s capital be X, then A’s capital = X + 1/3 × X = 4/3 × X = 4X/3

Investment of A for 1 year = 4X/3 for 5 months + (4X/3 – 50% of 4X/3) for 7 months = 4X/3 × 5 + (4X/3 – 2X/3) × 7

⇒ 20X/3 + 14X/3 = 34X/3

Investment of B for 1 year = X for 8 months + (X – 1/3 × X) for 4 months = 8X + 2X/3 × 4

⇒ 8X + 8X/3 = 32X/3

Ratio of profit = 34X/3 ∶ 32X/3 = 34 ∶ 32 = 17 ∶ 16

∴ Ratio of profit would be 17 ∶ 16.