JIPMAT 2021 (QA) - 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 | PYQs + Solutions | AfterBoards
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JIPMAT 2021

Arithmetic
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Ratio, Proportion & Variation

Conceptual

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

Correct Option: 2
First ratio =4:3:2:1=4:3:2:1, sum of parts =10= 10\newlineSecond ratio =5:6:7:8=5:6:7:8, sum of parts = 2626
Let first sum = xx\newlineSecond sum = 2x2x (given)
Distribution of first sum (xx):\newline- Naresh (44): 4x10\frac{4x}{10}\newline- Vipin (33): 3x10\frac{3x}{10}\newline- Bhupesh (22): 2x10\frac{2x}{10}\newline- Yogesh (11): x10\frac{x}{10}
Distribution of second sum (2x2x):\newline- Naresh (55): 10x26\frac{10x}{26}\newline- Vipin (66): 12x26\frac{12x}{26}\newline- Bhupesh (77): 14x26\frac{14x}{26}\newline- Yogesh (88): 16x26\frac{16x}{26}
Total for each:\newlineNaresh: x(410+1026)=x(104+100260)=x(204260)x(\frac{4}{10} + \frac{10}{26}) = x(\frac{104 + 100}{260}) = x(\frac{204}{260})
Vipin: x(310+1226)=x(78+120260)=x(198260)x(\frac{3}{10} + \frac{12}{26}) = x(\frac{78 + 120}{260}) = x(\frac{198}{260})
Bhupesh: x(210+1426)=x(52+140260)=x(192260)x(\frac{2}{10} + \frac{14}{26}) = x(\frac{52 + 140}{260}) = x(\frac{192}{260})
Yogesh: x(110+1626)=x(26+160260)=x(186260)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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