Question

How many more coins did each boy get than each girl?

• A. 3
• B. 5
• C. 4
• D. 6
• E. None

Answer 1

The correct option is D 6

Given, there are a total of 200 coins in two bags and granddaughters pick the bag which have more number of coins than the bag which grandsons has.
Also, given there are 9 granddaughters and 5 grandsons.
Now, suppose each of the girl get 10 coins, then total coins get by girls = 9 X 10 = 90 coins. Also, 2 coins are given to charity and 1 coin is given to boys.
So, girls has 93 coins in their bag and boys has 200 - 93 = 107 coins.
Now, boys get one coin from the girls so, total number of coins with boys = 107 + 1 = 108
which can't be distributed equally among 5 boys.
Therefore, our supposition is incorrect.
Now, let us suppose that each girl get 11 coins, then total coins get by girls = 9 X 11 = 99 coins. Also, 2 coins are given to charity and 1 coin is given to boys.
So, girls has 102 coins in their bag and boys has 200 - 102 = 98.
Now, boys get one coin from the girls so, total number of coins with boys = 98 + 1 = 99
coins which again can't be distributed equally among 5 boys.
Therefore, our supposition is again incorrect.
Again, let us suppose that each girl get 12 coins, then total coins get by girls = 9 X 12 = 108 coins. Also, 2 coins are given to charity and 1 coin is given to boys.
So, girls has 111 coins in their bag therefore, boys has 200 - 111 = 89 coins.
Now, boys get one coin from the girls so, total number of coins with boys = 89 + 1 = 90 which are easily distributed among 5 grandsons as: 905=18
So, each boy will get 18 coins when each girl get 12 coins.
Clearly, a boy get 6 more coins than a girl.