Question

At present, the average age of a father and his son is 29 years. the average age of father, mother and son five years from now will be 37 years. find the mother's present age.

Answer 1

kindly check the calculation otherwise the concept is right

Answer 2

Answer:

The present age of mother is equal to 38 years.

Step-by-step explanation:

Consider that X, Y and Z are present age of father, son and mother respectively.

Give, the average age of a father (X) and his son (Y) is 29 years.

$\frac{X+Y}{2} =29$

$X+Y = 58$

$X = 58-Y$                                                                         .................(1)

After 5 years, the average age of father, mother and son will be 37 years.

After 5 years, the age of father will be = X + 5

After 5 years, the age of son $= Y + 5$

The age of mother  will be = Z + 5

Therefore, we can write this as:

$\frac{X+5+Y+5+Z+5}{3}=37$

$X+Y+Z+15 = 111$

$X+Y+Z=96$

Substitute the value of X from equation (1) in above equation:

$(58-Y)+Y+Z=96$

$Z= 96-58$

$Z= 38$

Therefore, the present age of the mother is equal to 38 years.

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