Question

A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3:2, while the ratio of the shares of Sunil and Mita is 4:5. If the difference between the largest and the smallest of these three shares is Rs 400, then Sunil’s share, in rupees, is
[This Question was asked as TITA]

• A. 800
• B. 650
• C. 970
• D. 680

Answer 1

The Correct Option is A

We are given the following ratios:

• Amal : Sunil = \(3 : 2\) 
• Sunil : Mita = \(4 : 5\)

To find the combined ratio of Amal : Sunil : Mita, we must make the Sunil part common in both ratios.

From the first ratio: Amal : Sunil = \(3 : 2\)

From the second ratio: Sunil : Mita = \(4 : 5\)

Make the Sunil parts equal in both by taking LCM of 2 and 4, which is 4.

So we multiply the first ratio by 2 and keep the second ratio as is:

\[ \text{Amal : Sunil : Mita} = (3 \times 2) : (2 \times 2) : (5 \times 1) = 6 : 4 : 5 \]

Now the total parts = \(6 + 4 + 5 = 15\)

If the total profit is ₹3000, then Sunil's share is:

\[ \text{Sunil's share} = \frac{4}{15} \times 3000 = ₹800 \]

Therefore, the correct option is (A): ₹800