Question

A certain number of chocolates are to be distributed among some boys. If one chocolate is given to each boy, then 8 chocolates will be leftover. If two chocolates are given to each boy, then one boy won't get any chocolate. Find the number of chocolates that have to be distributed. *

Answer 1

Given: If one chocolate is given to each boy, then 8 chocolates will be leftover

If two chocolates are given to each boy, then one boy won't get any chocolate

To Find: The number of chocolates that have to be distributed

Solution:

Let the number of boys be x

Let the total number of chocolates be y

If one chocolate is given to each boy, then 8 chocolates will be leftover. This can be represented as

y = x + 8                     ....1

If two chocolates are given to each boy, then one boy won't get any chocolate. This situation can be represented as

y = 2(x-1)                   ...2

On comparing eq 1 and 2

x + 8 = 2 (x-1)

x + 8 = 2x - 2

8 + 2 = 2x - x

10 = x

Putting the value of x in equation 1

y = 10 + 8

y = 18

Therefore, the number of chocolates to be distributed is 18.