Question

A, B and C together invests Rs. 53,000 in a business. A invests Rs. 5,000 more than B and B invests Rs. 6,000 more than C. Out of a total profit of Rs. 31,800, find the share of A.
1. Rs. 12,500
2. Rs. 13,800
3. Rs. 12,80
4. Rs. 13,500

Answer 1

Correct Answer - Option 2 : Rs. 13,800

Given:
Investment of A, B and C together = Rs. 53,000
Investment of A = Investment of B + Rs. 5,000 
Investment of B = Investment of C + Rs. 6,000
Total profit of A, B and C together = Rs. 31800

Concept used:
If time is not given, then the investment ratio is directly proportional to the profit ratio.

Calculation:
Let the investment of C be x.
Investment of B = x + 6000
Investment of A = x + 6000 + 5000
Total investment = 53000 
⇒ x + x + 6000 + x + 6000 + 5000 = 53000
⇒ 3x + 17000 = 53000
⇒ 3x = 53000 – 17000
⇒ 3x = 36000
⇒ x = 36000/3
⇒ x = 12000
Investment of A = 12000 + 11000 = 23000
Investment of B = 12000 + 6000 = 18000
Investment of C = 12000
Ratio of investment of A, B and C = 23000 : 18000 : 12000
⇒ 23 : 18 : 12
Share of A = (23/53) × 31800
⇒ 23 × 600
⇒ 13800
∴ The share of A is Rs. 13800.