Question

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?

• A. Q
• B. T
• C. R
• D. S

Hint:

Compare each person's share before and after squaring the ratio terms.

Answer 1

The Correct Option is B

Step 1: Find the original shares. The ratio 1 : 1.5 : 2 : 2.5 : 3 has a sum of parts \(1+1.5+2+2.5+3=10\). So the original fractional shares are P = 0.10, Q = 0.15, R = 0.20, S = 0.25, T = 0.30.
Step 2: Find the duplicate ratio. The duplicate ratio squares each term: \(1^2 : 1.5^2 : 2^2 : 2.5^2 : 3^2 = 1 : 2.25 : 4 : 6.25 : 9\), with sum of parts \(1+2.25+4+6.25+9=22.5\).
Step 3: Find the new shares. P = 1/22.5 ≈ 0.0444, Q = 2.25/22.5 = 0.10, R = 4/22.5 ≈ 0.1778, S = 6.25/22.5 ≈ 0.2778, T = 9/22.5 = 0.40.
Step 4: Compare the change for each person. P: 0.0444 - 0.10 = -0.0556 (loss). Q: 0.10 - 0.15 = -0.05 (loss). R: 0.1778 - 0.20 = -0.0222 (loss). S: 0.2778 - 0.25 = +0.0278 (small gain). T: 0.40 - 0.30 = +0.10 (largest gain).
Step 5: Identify who benefits the most. T's share increases the most, by 10 percentage points, so T benefits the most.\[\boxed{T}\]