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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 $\text{Rs.} 400,$ then Sunil’s share, in rupees, is

Given that,

The ratio of shares$:$

• Amal : Sunil $= 3 : 2$
• Sunil : Mita $= 4 : 5$

Now, combining the ratio.

• Amal : Sunill $= (3:2) \times 4 = 12 : 8$
• Sunil : Mita $= (4:5) \times 2 = 8 : 10$

$\boxed { \text{Amal} : \text{Sunil} : \text{Mita} = 12 : 8 : 10 = 6 : 4 : 5}$

Let the shares of Amal, Sunil, and Mita be $6x, 4x,$ and $5x.$

Now, $6x – 4x = 400$

$\Rightarrow 2x = 400$

$\Rightarrow \boxed{x = 200}$

So, the share of Sunil $= 4x = 4(200) = \text{Rs.}\;800$

$\therefore$ The share of Sunil is $\text{Rs.}\;800.$

Correct Answer $: 800$

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