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

Entered answer:

✅ Correct Answer: 800

We have three people sharing money with two separate ratio conditions:

Amal : Sunil = 3 : 2

Sunil : Mita = 4 : 5

The key insight is that we need to combine these ratios to find a single ratio for all three people.

Sunil appears in both ratios with different values (2 in the first ratio, 4 in the second).

Make Sunil's part equal in both ratios by finding the LCM.

LCM of 2 and 4 = 4

First ratio: Amal : Sunil = 3 : 2

Multiply by 2: Amal : Sunil = 6 : 4

Second ratio: Sunil : Mita = 4 : 5

Already has Sunil = 4, so no change needed

Combined ratio: Amal : Sunil : Mita = 6 : 4 : 5

Let the shares be:

Amal's share = $6x$

Sunil's share = $4x$

Mita's share = $5x$

Which is the largest share? $6x$ (Amal's)

Which is the smallest share? $4x$ (Sunil's)

Since $6x > 5x > 4x$ , the difference between largest and smallest is $6x - 4x$ .

Given: Difference = Rs 400

Therefore: $6x - 4x = 400$

$2x = 400$

$x = 200$

Sunil's share = $4x = 4 \times 200 = \text{Rs } 800$

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