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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Compare each person's share before and after squaring the ratio terms.
Updated On: Jul 21, 2026
  • Q
  • T
  • R
  • S
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The Correct Option is B

Solution and Explanation

This can be answered quickly, without computing every share, by looking at how much each person's share grows relative to their original share.
Step 1: Write the general shares. If the sum of the original ratio terms is \(S_1 = 10\) and the sum of the squared (duplicate) terms is \(S_2 = 22.5\), then for a person with original term t, the original share is \(t/S_1\) and the new share is \(t^2/S_2\).
Step 2: Find the growth factor for each person. The ratio of new share to old share is \(\dfrac{t^2/S_2}{t/S_1} = \dfrac{t \times S_1}{S_2} = t \times \dfrac{10}{22.5}\), which is directly proportional to t itself.
Step 3: Interpret this. Since the growth factor is proportional to the person's own original ratio term, whoever had the LARGEST original term will see their share grow by the largest factor, meaning they benefit the most in absolute terms as well (since they also start from the largest base).
Step 4: Identify the largest original term. Among P(1), Q(1.5), R(2), S(2.5), T(3), T has the largest term, 3, so T benefits the most from the change to duplicate ratio.\[\boxed{T}\]
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