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

Answer 1

Step 1: Combine the Two Ratios 

We are given: \[ \text{Amal : Sunil} = 3 : 2 \quad \text{(i)} \] \[ \text{Sunil : Mita} = 4 : 5 \quad \text{(ii)} \] To combine them, make Sunil’s parts equal in both ratios. LCM of 2 and 4 is 4. So rewrite the ratios: \[ \text{Amal : Sunil} = 6 : 4 \quad \text{(multiply both terms by 2)} \] \[ \text{Sunil : Mita} = 4 : 5 \] Now combine: \[ \text{Amal : Sunil : Mita} = 6 : 4 : 5 \]

Step 2: Use Given Value

Mita’s share = ₹400 So the share units are: \[ \text{Total parts} = 6 + 4 + 5 = 15 \] Each part = \[ \frac{400}{5} = 80 \] So Sunil’s share (4 parts) is: \[ 4 \times 80 = \boxed{₹320} \]

Final Answer:

Sunil’s share is ₹320