What is the difference between the numbers of coins in the two bags?

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Solution

The correct option is A 22
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: $90 \div 5 = 18$
So, each boy will get 18 coins when each girl get 12 coins.
Therefore, the girls bag have 111 coins in it and boys bags have 89 coins in it.
Clearly, the difference in number of coins of two bags = 111 - 89 = 22 coins

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