Aakash, Vikas and Rajan start a business by investing capital in the ratio 5 : 6 : 8. At the end they receive the profit in the ratio 5 : 3 : 12. Find the ratio Aakash : Vikas : Rajan of the times for which their capital was used.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2 : 1 : 3
Profit \(=\) capital \(\times\) time (in ratio), so each partner’s time is in the ratio of profit ÷ capital.
Aakash: \(\frac{5}{5}=1\)
Vikas: \(\frac{3}{6}=\frac{1}{2}\)
Rajan: \(\frac{12}{8}=\frac{3}{2}\)
Aakash : Vikas : Rajan \(=1:\frac{1}{2}:\frac{3}{2}\); multiplying by 2 gives \(2:1:3\)
The times are in the ratio Aakash : Vikas : Rajan = 2 : 1 : 3.