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

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&rsquo;s share, in rupees, is

Accepted Answer

800 — Easy Combine the two pairwise ratios into a single three-way ratio by making Sunil's part common, then translate "difference of largest and smallest = 400" into one equation for the scale factor. 1 Merge the ratios. Amal : Sunil $=3:2$ and Sunil : Mita $=4:5$. Scale the first by $2$ so Sunil matches. $$\begin{aligned} &A:S = 3:2 = 6:4\ &S:M = 4:5\ &\Rightarrow\ A:S:M = 6:4:5 \end{aligned}$$ 2 Use the difference. Let the parts be $6x,4x,5x$. Largest is Amal ($6x$), smallest is Sunil ($4x$). $$\

CAT 2020 Slot 2 — QA Question 7

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