Discussion

Explanation:

Let their investments be Rs. x for 14 months, Rs. y for 7 months and Rs. z for 8 months respectively.

We know, Profit ∝ Investment × Time

Hence, ratio of their profit, 5 : 8 : 7 = 14x : 7y : 8z.

Now, 14x/7y = 5/8 ⇒ y = 16/5 x

And, 14x/8z = 5/7 ⇒ z = 49/20 x

∴ x ∶ y ∶ z = x ∶ 16/5 x ∶ 49/20 x = 20 ∶ 64 ∶ 49

Alternately,

We know, ratio of their profit, 5 : 8 : 7 = 14x : 7y : 8z.

⇒ x : y : z = $\frac{5}{14}:\frac{8}{7}:\frac{7}{8}$= $\frac{56\times 5}{14}:\frac{56\times 8}{7}:\frac{56\times 7}{8}$ = 20 : 64 : 49

Hence, option (c).

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