The Social Problem 3

Algebra Level 2

Three boys were given a bag of candies as a Diwali present, and it was agreed that they should be divided in proportion to their ages, which together amounted to 17½ years.

Now the bag contained 770 candies, and as often as Atish took four Pranav took three, and as often as Atish took six Maninder took seven.

How many candies did Pranav took and what is his age?

198 and 4 years, 6 months 308 and 7 years 264 and 8 years 264 and 6 years

1 solution

Hung Woei Neoh
Apr 16, 2016

The ratio of age between Pranav, Atish and Maninder is exactly the same as the ratio of candies they get.

Now, we know that Pranav : Atish $=3:4$ and Atish : Maninder $=6:7$

What we need to do here is to find Pranav : Atish : Maninder. Therefore, we need to find a common multiple for Atish in both ratios. The common multiple for $4$ and $6$ is $12$ . Multiply accordingly, and you should get:

Pranav : Atish $=3:4 = 9:12$

Atish : Maninder $=6:7 = 12:14$

Therefore, Pranav : Atish : Maninder $=9:12:14$

With this, we can calculate the amount of candy Pranav took and Pranav's age:

Amount of candy $=\dfrac{9}{9+12+14} \times 770 = \boxed{198 \;\text{candies}}$

Age $=\dfrac{9}{9+12+14} \times 17\dfrac{1}{2} = 4\dfrac{1}{2} = \boxed{4\;\text{years}\;6\;\text{months}}$

The Social Problem 3

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