Question:medium

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]

Updated On: Jan 15, 2026
  • 800
  • 650
  • 970
  • 680
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The Correct Option is A

Solution and Explanation

Given the ratios:

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

To determine the combined ratio of Amal : Sunil : Mita, the value representing Sunil must be standardized across both ratios.

The initial ratios are:

Amal : Sunil = \(3 : 2\)

Sunil : Mita = \(4 : 5\)

The least common multiple (LCM) of the Sunil values (2 and 4) is 4. This value will be used to unify the ratios.

Multiply the first ratio by 2 and retain the second ratio unchanged:

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

The sum of these parts is \(6 + 4 + 5 = 15\).

Given a total profit of ₹3000, Sunil's allocated share is calculated as:

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

The corresponding option is (A): ₹800

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