Question

Sum of ages of mother and son before 5 years was y years. Sum
of their ages after 5 years will be —————————— years.

Answer 1

Answer:

It's very obvious that age of an individual person will increase by 1 with every year.

Every year, sum of increased age of 5 people will be 5 years.

Every 5 years, sum of increased age of 5 people will be 5x5 = 25 years.

Based on above understanding,

sum of age of 5 people as of current year will be = sum of age of 5 people before 5 years + sum of increased age of 5 people in 5 years = 50 + 25 = 75 and after 5 years from current year, it will be 75 + 25 = 100 years.

Answer 2

Given: Sum of ages of mother and son 5 years ago = y

To find: Sum of their ages after 5 years

Let: Present age of mother = x years

      Present age of son = z years

Solution: According to the given question,

5 years ago, sum of ages of mother and son = y

If mother's present age is x and son's present age is z. Then, 5 years ago, their ages must have been (x - 5) and (z - 5) respectively.

i.e., (x - 5) + (z - 5) = y

⇒ x - 5 + z - 5 = y

⇒ x + z - 10 = y

⇒ x + z = y + 10                                              ...(1)

After 5 years, their ages will be (x + 5) and (z + 5)

Sum of their ages after 5 years will be = x + 5 + z + 5

= x + z + 10

Putting value of (x + z) from equation (1)

= (y + 10) + 10

= y + 20

Therefore, after 5 years sum of their ages will be (y + 20)