Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had

Question

Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?

Options:

A . 5 : 7 : 8

B . 20 : 49 : 64

C . 38 : 28 : 21

D . None of these

Answer: Option B

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

Then, 14x : 8y : 7z = 5 : 7 : 8.

Now, \(\frac{14x}{8y} = \frac{5}{7} \Leftrightarrow 98x=40y \Leftrightarrow y = \frac{49}{20}x \)

And , \(\frac{14x}{7z} = 112x = 35z \Leftrightarrow z = \frac{112}{35} =\frac{16}{5}x.\)

Therefore x : y : z = x : \(\frac{49}{20}x:\frac{16}{5}x\) = 20 : 49 : 64.

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