Question 105

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 ?

Solution

Case I = A : B : C = $$\frac{1}{5}:\frac{1}{4}:\frac{1}{8}$$

L.C.M. (5,4,8) = 40

= $$\frac{40}{5}:\frac{40}{4}:\frac{40}{8}=8:10:5$$

Sum of terms of ratio = $$8+10+5=23$$

Case II = A : B : C = $$5:4:8$$

Sum of term of ratio = $$5+4+8=17$$

Clearly, only C gains by = $$(\frac{8}{17}-\frac{5}{23})\times391$$

= $$\frac{184-85}{391}\times391=99$$

=> Ans - (C)

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