Question : A, B, and C invested capital in the ratio of 3 : 4 : 8. At the end of the business term, they received the profit in the ratio of 2 : 3 : 5. What is the ratio of their invested time?
Option 1: 15 : 16 : 13
Option 2: 13 : 18 : 15
Option 3: 16 : 18 : 15
Option 4: 16 : 21 : 18
Correct Answer: 16 : 18 : 15
Solution :
The ratio of A, B, and C's capitals is 3 : 4 : 8.
They received the profit in the ratio of 2 : 3 : 5.
Let the time invested by A, B, and C be x, y and z respectively.
We know: Capital ratio × Time ratio = Profit ratio
So, 3x = 2 ⇒ x = $\frac{2}{3}$
4y = 3 ⇒ y = $\frac{3}{4}$
8z = 5 ⇒ z = $\frac{5}{8}$
$\therefore$ x : y : z = $\frac{2}{3} :\frac{3}{4}:\frac{5}{8}$
Taking LCM of 3, 4, 8 = 24
x : y : z $=\frac{2}{3} ×24:\frac{3}{4}×24:\frac{5}{8}×24=16:18:15$
Hence, the correct answer is 16 : 18: 15.
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