Question : 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 into the ratio $5:4:8$. Who gains most and how many?
Option 1: A, 21 cookies
Option 2: B, 78 cookies
Option 3: C, 99 cookies
Option 4: C, 78 cookies
Correct Answer: C, 99 cookies
Solution :
Case 1:
A : B : C = $\frac{1}{5}:\frac{1}{4}:\frac{1}{8}$
LCM of 5, 4, and 8 is 40.
So, A : B : C = $\frac{1}{5}×40:\frac{1}{4}×40:\frac{1}{8}×40$ = 8 : 10 : 5
Sum of A + B + C = 8 + 10 + 5 = 23
Case 2:
A : B : C = 5 : 4 : 8
Sum of A + B + C = 5 + 4 + 8 = 17
Clearly, C gains.
C's profit = $(\frac{8}{17}-\frac{5}{23})$ × 391
= $\frac{8}{17}×391-\frac{5}{23}×391$
= $184-85$
= $99$
Hence, the correct answer is C, 99 cookies.
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