What will be the share of R in the profit earned by V, R, and A together?
Given the following statements:

I. They together earned a profit of Rs. 54,000 for a period of 1 year.

II. R’s investment was 25\% less than V’s and 50\% more than A’s.

III. The profit of V is Rs. 4,000 more than that of A.

Which of the following options is correct?

Question

What will be the share of R in the profit earned by V, R, and A together?
Given the following statements:

I. They together earned a profit of Rs. 54,000 for a period of 1 year.

II. R’s investment was 25\% less than V’s and 50\% more than A’s.

III. The profit of V is Rs. 4,000 more than that of A.

Which of the following options is correct?

Accepted Answer

**Solution:**

1. From statement I, the total profit earned by V, R, and A together is Rs. 54,000 for 1 year.

2. Statement II provides the relationship between their investments:
   - R’s investment is 25\% less than V’s, so if V’s investment is $x$, then R’s investment is $0.75x$.
   - R’s investment is also 50\% more than A’s, so if A’s investment is $y$, then R’s investment is $1.5y$.

3. Equate R’s investment from both expressions:
   $$0.75x = 1.5y \implies x : y = 2 : 1$$

4. Therefore, the investment ratio of V : R : A is:
   $$x : 0.75x : y = 2 : 1.5 : 1$$
   Multiplying all by 2 to clear decimals:
   $$4 : 3 : 2$$

5. From statement III, the profit of V is Rs. 4,000 more than that of A.
   Let the profit share of A be $2k$, then profit of V is $4k$.

6. Using the profit ratio equal to investment ratio (since time is 1 year):
   $$\text{Profit of V} = 4k, \quad \text{Profit of A} = 2k$$
   Given:
   $$4k = 2k + 4000 \implies 2k = 4000 \implies k = 2000$$

7. Hence, profit of A = $2 \times 2000 = 4000$, profit of V = $4 \times 2000 = 8000$.

8. Total profit is Rs. 54,000, so profit of R = $54,000 - (8,000 + 4,000) = 42,000$.

9. Therefore, using statements II and either I or III, we can find R’s share in the profit.

**Answer:** (b) II and either I or III only

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