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?

5 : 7 : 8

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20 : 49 : 64

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38 : 28 : 21

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None of these

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Solution

The correct option is D $20 : 49 : 64$
Let their investments be Rs. $x$ for $14$ months, Rs. $y$ for $8$ months and Rs. $z$ for $7$ months respectively.
Then, $14 x : 8 y : 7 z = 5 : 7 : 8$ .
Now, $\frac{14 x}{8 y} = \frac{5}{7} \Leftrightarrow 98 x = 40 y \Leftrightarrow y = \frac{49}{20} x$
And, $\frac{14 x}{7 z} = \frac{5}{8} \Leftrightarrow 112 x = 35 z \Leftrightarrow z = \frac{112}{35} x = \frac{16}{5} x$ .
$∴ x : y : z = x : \frac{49}{20} x : \frac{16}{5} x = 20 : 49 : 64$ .

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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?

The correct option is D 20:49:64Let 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, 14x8y=57⇔98x=40y⇔y=4920xAnd, 14x7z=58⇔112x=35z⇔z=11235x=165x.∴x:y:z=x:4920x:165x=20:49:64.

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?