Question

Two friends A and B invest in a business in partnership, B borrows 20% of A's salary, combines it with 60% of his salary and invest with A, who puts all of his remaining salary. One year later the ratio of profit A and B is 5:3 respectively and B returns Rs. 21000 to A which he borrowed from him. What is the difference between salary of A and B ?

• A. Rs 56000
• B. Rs 32000
• C. Rs 60000
• D. Rs 28000

Answer 1

The Correct Option is A

Let the salary of A be Rs. a and the salary of B be Rs. b.

B borrows 20% of A's salary = Rs. 0.2a.

B invests this with 60% of his salary = Rs. 0.6b.

Total investment by B = 0.2a + 0.6b.

A invests the remaining 80% of his salary = Rs. 0.8a.

After one year, the ratio of profit between A and B is 5:3.

Since profit is in the ratio of their investments, we have:

\(\frac{0.8a}{0.2a + 0.6b} = \frac{5}{3}\)

Cross multiplying gives:

3 × 0.8a = 5(0.2a + 0.6b)

\(2.4a = 1a + 3b\)

Solving, \(1.4a = 3b\) or \(a = \frac{3}{1.4}b\)

Now, we know B returned Rs. 21000 to A, which he borrowed.

Thus, 0.2a = 21000

From this, \(a = \frac{21000}{0.2} = 105000\)

Substitute it back into the equation:

105000 = \(\frac{3}{1.4}b\)

Solving for b, \(b = 49000 \times \frac{3}{1.4} = 49000 × \frac{3}{1.4} = 49000 × \frac{3×10}{14} = 49000 × \frac{30}{14} = 49000 × \frac{15}{7} = 105000 × \frac{15}{7}\approx 49000 × 2.142857 = 105000\)

The difference between the salaries of A and B is:

\(105000 - 49000 = 56000\)

Salary Difference

Rs 56000