Arithmetic

Ratio, Proportion & Variation

Medium

Harish divides two sums of money among his four sons Naresh, Vipin, Bhupesh, and Yogesh. The first sum is divided in the ratio $4:3:2:1$ and second in the ratio $5:6:7:8$ . If the second sum is twice the first, then the largest total is received by

Bhupesh

Naresh

Vipin

Yogesh

✅ Correct Option: 2

First ratio $=4:3:2:1$ , sum of parts $= 10$

Second ratio $=5:6:7:8$ , sum of parts = $26$

Let first sum = $x$

Second sum = $2x$ (given)

Distribution of first sum ( $x$ ):

Naresh ( $4$ ): $\frac{4x}{10}$
Vipin ( $3$ ): $\frac{3x}{10}$
Bhupesh ( $2$ ): $\frac{2x}{10}$
Yogesh ( $1$ ): $\frac{x}{10}$

Distribution of second sum ( $2x$ ):

Naresh ( $5$ ): $\frac{10x}{26}$
Vipin ( $6$ ): $\frac{12x}{26}$
Bhupesh ( $7$ ): $\frac{14x}{26}$
Yogesh ( $8$ ): $\frac{16x}{26}$

Total for each:

Naresh: $x(\frac{4}{10} + \frac{10}{26}) = x(\frac{104 + 100}{260}) = x(\frac{204}{260})$

Vipin: $x(\frac{3}{10} + \frac{12}{26}) = x(\frac{78 + 120}{260}) = x(\frac{198}{260})$

Bhupesh: $x(\frac{2}{10} + \frac{14}{26}) = x(\frac{52 + 140}{260}) = x(\frac{192}{260})$

Yogesh: $x(\frac{1}{10} + \frac{16}{26}) = x(\frac{26 + 160}{260}) = x(\frac{186}{260})$

The biggest value of the fractions above will be the one with the largest numerator.

Therefore, Naresh receives the largest total.

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Harish divides two sums of money among his four sons Naresh, Vipin, Bhupesh, and Yogesh. The first sum is divided in the ratio 4:3:2:14:3:2:14:3:2:1 and second in the ratio 5:6:7:85:6:7:85:6:7:8. If the second sum is twice the first, then the largest total is received by

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Harish divides two sums of money among his four sons Naresh, Vipin, Bhupesh, and Yogesh. The first sum is divided in the ratio $4:3:2:1$ and second in the ratio $5:6:7:8$ . If the second sum is twice the first, then the largest total is received by