A sum of Rs 2156 was to be divided among P, Q, R and S in the ratio 2 : 3 : 4 : 5, but it was divided in the ratio \(\frac{1}{2}:\frac{1}{3}:\frac{1}{4}:\frac{1}{5}\) instead. Which of the following is true?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → R received Rs 196 less
Work out each person's share under both ratios and compare. The fraction ratio becomes whole numbers when multiplied by 60, the LCM of 2, 3, 4 and 5.
Planned: \(2+3+4+5=14\) parts, 1 part \(\displaystyle =\frac{2156}{14}=\) Rs 154; shares Rs 308, Rs 462, Rs 616, Rs 770
Actual ratio: \(\displaystyle \frac{1}{2}:\frac{1}{3}:\frac{1}{4}:\frac{1}{5}=30:20:15:12\), 77 parts
1 part \(\displaystyle =\frac{2156}{77}=\) Rs 28; shares Rs 840, Rs 560, Rs 420, Rs 336
R: \(616-420=\) Rs 196 less
Why the other options are incorrect
Option (1) P received Rs 534 more — Incorrect. P received \(840-308=\) Rs 532 more.
Option (2) Q received Rs 90 more — Incorrect. Q received \(560-462=\) Rs 98 more.
Option (4) S received Rs 440 less — Incorrect. S received \(770-336=\) Rs 434 less.