Three partners shared the profit of a business in the ratio 5 : 7 : 8. They kept their capital in the business for 14 months, 8 months and 7 months respectively. What was the ratio of their capitals, in the same order?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 20 : 49 : 64
Profit \(\propto\) capital × months, so each capital is in proportion to profit share ÷ months.
Capitals \(\displaystyle =\frac{5}{14}:\frac{7}{8}:\frac{8}{7}\)
Multiplying by 56 (the LCM of 14, 8 and 7): \(\displaystyle \frac{5}{14}\times56=20\), \(\displaystyle \frac{7}{8}\times56=49\), \(\displaystyle \frac{8}{7}\times56=64\)
Capitals \(=20:49:64\)
The capitals were in the ratio 20 : 49 : 64.
Why the other options are incorrect
Option (1) 5 : 7 : 8 — Incorrect. This is the profit ratio; it would be the capital ratio only if all three stayed for the same time.
Option (3) 38 : 28 : 21 — Incorrect. It gives the first partner the largest capital, but he earned the smallest profit while staying the longest.
Option (4) None of these — Incorrect. The ratio 20 : 49 : 64 is given in Option (2).