Instead of dividing 391 cookies among 3 children A , B,C in ratio frac{1}{5}: frac{1}{4}: frac{1}{8}

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7.Profit and Loss

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Instead of dividing $391$ cookies among $3$ children $A$, $B,C$ in the ratio $\frac{1}{5}: \frac{1}{4}: \frac{1}{8},$ it was divided in to the ratio $5: 4: 8 .$ Who gains the most and how many?

A

$A, 21$ cookies

B

$B, 78$ cookies

C

$C, 99$ cookies

D

$C, 78$ cookies

Solution

Actual Ratio $\Rightarrow A: B: C \Rightarrow \frac{1}{5}: \frac{1}{4}: \frac{1}{8} \Rightarrow 8: 10: 5$

$A$ 's share $=\frac{8}{23} \times 391=136$

$B$ 's share $=170$

$C^{\prime} s$ share $=85$

It was divided in the Ratio $\Rightarrow A: B: C \Rightarrow 5: 4: 8$

$A$ 's share $=\frac{5}{17} \times 391=115$

$B$ 's share $=92$

$C s$ share $=184$

$C$ Gains more $=184-85=99$ cookies

Standard 13

Quantitative Aptitude

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