Kiran, Deepak and Farhan invested Rs 8,000, Rs 12,000 and Rs 16,000 for 2 years, 3 years and 6 months respectively. Find the ratio Kiran : Deepak : Farhan of their profits at the end.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 : 9 : 2
When the money stays in for different periods, the profit is shared in the ratio of capital × time, with all the times in the same unit; 6 months is half a year.
Kiran: \(8000\times2=16000\)
Deepak: \(12000\times3=36000\)
Farhan: \(16000\times\frac{1}{2}=8000\)
\(16000:36000:8000\); dividing by 4000 gives \(4:9:2\)
The profits are in the ratio Kiran : Deepak : Farhan = 4 : 9 : 2.
Why the other options are incorrect
Option (1) 2 : 9 : 4 — Incorrect. This swaps Kiran’s and Farhan’s shares; Farhan’s money stayed only half a year.
Option (3) 3 : 4 : 5 — Incorrect. It does not match the capital × time products 16000, 36000 and 8000.
Option (4) 9 : 2 : 3 — Incorrect. It gives Kiran the largest share, but Deepak has the largest capital × time, 36000.