# 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. 40

B. 46

C. 50

D. 60

Answer

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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 father’s age 2 years ago is ‘f’

Mother’s age 2 years ago be ‘m’

First daughter’s age be d1 second daughter’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 ……(i)

Their present ages will be calculated by adding 2 in all their ages.

Father’s present age = f + 2

Mother’s present age = m + 2

First daughter’s present age = d1 + 2

Second daughter’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, everybody’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.

Firstly, let us assume the variables of their ages 2 years ago.

Let us assume that the father’s age 2 years ago is ‘f’

Mother’s age 2 years ago be ‘m’

First daughter’s age be d1 second daughter’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 ……(i)

Their present ages will be calculated by adding 2 in all their ages.

Father’s present age = f + 2

Mother’s present age = m + 2

First daughter’s present age = d1 + 2

Second daughter’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, everybody’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.

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