Question

# 2 years ago, the addition of age of a father-mother and their two daughters was 40 years. After 3 years the addition of their ages will be.............. A. 40B. 46C. 50D. 60

Hint: In order to solve this problem we will sum up all their ages of 2 years ago and then will calculate the sum of their present ages by adding 2 in all their ages then we will add 3 in all their ages to get the sum of their age after 3 years.

Firstly, let us assume the variables of their ages 2 years ago.
Let us assume that the fatherâ€™s age 2 years ago is â€˜fâ€™
Motherâ€™s age 2 years ago be â€˜mâ€™
First daughterâ€™s age be d1 second daughterâ€™s age be d2.
It is given that the sum of their ages two years ago is 40 years. So, we can do :
f + m + d1 + d2 = 40 â€¦â€¦(i)
Their present ages will be calculated by adding 2 in all their ages.
Fatherâ€™s present age = f + 2
Motherâ€™s present age = m + 2
First daughterâ€™s present age = d1 + 2
Second daughterâ€™s present age = d2 + 2
On adding the present ages of all of them we get,
f + 2 + m + 2 + d1 + 2 + d2 + 2 = P (say) (let the sum of their present ages be P)
On solving the above equation further we get,
f + m + d1 + d2 + 8 = P
From the equation (i) we know f + m + d1 + d2 = 40
So,
40 + 8 = P
Therefore, P = 48.
So, we come to know that the sum of their present ages is 48.
But we have to calculate the sum of their ages 3 years from now.
So, we will add 3 four times in their present age. We will add 3 four times because there are four persons whose present age we have and we have to calculate the sum of their ages 3 years from now. So, everybodyâ€™s age will increase by 3 therefore we will add 3 four times the sum of their present age to get the sum of their age 3 years from now.
Sum of their present age is 48.
Sum of their ages 3 years from now will be 48 + 3 + 3 + 3 + 3 = 48 + 12 = 60 years
Therefore the sum of their ages after 3 years will be 60 years.
Hence, the correct option is D.

Note: In this problem we have assumed the variables of their ages 2 years ago. The sum of their ages 2 years ago is given then we have added 2 four times to get the sum of their present ages. Then we have added 3 four times their present age to get the sum of their ages after three year. Doing this will take you to the right answer.