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As a new year gift, three boys got a bag of chocolates. To divide the 770 chocolates in the bag, the boys worked out a formula. They would divide the chocolates in proportion to their ages. Now the boys, whose sum of ages amounted to 17½ years, carried out the following division:
1. every time Hitesh took 4 chocolates, Rajan took 3
2. every time Hitesh took 6 chocolates, Chetan took seven.
How many chocolates did each boy get, and what were their ages?

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We can see that when Hitesh takes 12 chocolates, Rajan gets 9, and Chetan gets 14. Taken together, this amounts to 35. As 770 is 35 x 22, we simply need to multiply 12, 9, 14 by 22 to discover their share: Hitesh: 264 Rajan: 198 Chetan: 308 As the sum of their ages is 17½ years and they take chocolates in proportion to their ages, we can simply see that we need to divide 12,9, 14 to obtain their ages. Their ages are: 6, 4½, and 7 years. Still confused how we arrived at the solution? This is question about factors. Start from the bottom, that is the ages, and work upwards to the total number of chocolates. You would see how all the numbers fit in.
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