Question:medium

A property was to be divided among P, Q, R, S and T in the ratio of \(1 : 1.5 : 2 : 2.5 : 3\). If instead, it was divided in the duplicate ratio, then who among the four would be benefitted most?

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Convert both ratios to a common total (20 for the original, 90 for the duplicate ratio) and compare each person's share as a fraction of the property before and after.
Updated On: Jul 20, 2026
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The Correct Option is B

Solution and Explanation

A quicker way is to compare growth factors instead of absolute shares.
Take the original ratio in lowest whole-number terms: \(2:3:4:5:6\), total \(=20\). The duplicate ratio is \(4:9:16:25:36\), total \(=90\).
For any person whose original part is \(k\), the new part is \(k^2\). Their share of the property changes from \(k/20\) to \(k^2/90\). The growth factor (new share divided by old share) is:
$$\frac{k^2/90}{k/20}=\frac{k}{90}\times 20=\frac{2k}{9}$$
This growth factor increases as \(k\) increases, so whoever has the LARGEST original part automatically gets the largest growth factor. Checking the parts \(k=2,3,4,5,6\) for P, Q, R, S, T respectively, T has the largest part (\(k=6\)), giving growth factor \(2(6)/9=12/9=4/3\approx1.33\), i.e. T's share grows by about 33%, more than anyone else. Since the ratio terms are all positive, the person with the highest original ratio value always benefits most when the ratio is duplicated, and here that person is T.\[\boxed{\text{T}}\]
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