Question 10

Reema had 'n' chocolates. She distributed them among 4 children in the ratio of $$\dfrac{1}{2} : \dfrac{1}{3} : \dfrac{1}{5} : \dfrac{1}{8}$$. If she gave them each one a complete chocolate, the minimum number of chocolates she had distributed.

Solution

The ratio in which Reema distributed chocolates = $$\dfrac{1}{2} : \dfrac{1}{3} : \dfrac{1}{5} : \dfrac{1}{8}$$

Now, $$LCM(2,3,5,8) = 120$$

So, the ratio in which Reema distributed chocolates = $$\dfrac{120}{2}:\dfrac{120}{3}:\dfrac{120}{5}:\dfrac{120}{8}=60:40:24:15$$

Let's say the common variable be $$x$$

So, the chocolates distributed by Reema = $$60x, 40x, 24x, 15x$$

So, total number of chocolates distributed = $$60x+40x+24x+15x$$ = $$139x$$

Now for minimum number of chocolates distributed, $$x$$ should be $$1$$.

So, minimum number of chocolates = $$139\times\ 1=139$$

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