Question

The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of husband is:
A.35 years
B.40 years
C.50 years
D.None of these

Answer 1

Hint: As we know, the average of the ages is the sum of the ages divided by the number of people. In this question, we need to calculate the present age of one person. To calculate this, we will find the sum of 3 person ages 3 years ago and then, sum of 2 person ages 5 years ago. In this way, we can get the sum of their present ages and we can simply subtract them to obtain the present age of one person.

Complete step-by-step answer:
According to the question, the average age of husband, wife and their child 3 years ago was 27 years.
We know, average = sum of their ages / number of persons
Let us assume their present ages:
Present age of the husband is H.
Present age of the wife is W.
Present age of the child is C.
Sum of their present ages $ = H + W + C$
Now, according to the data given in question, for 3 years ago
Sum of their ages will be $\left( {H - 3} \right) + \left( {W - 3} \right) + \left( {C - 3} \right) = H + W + C - 9$
We have average = 27
Using formula for average, we get
\[
  A = \dfrac{{H + W + C - 9}}{3} \\
\Rightarrow 27 = \dfrac{{H + W + C - 9}}{3} \\
\Rightarrow 27 \times 3 = H + W + C - 9 \\
\Rightarrow 81 + 9 = H + W + C \\
\Rightarrow 90 = H + W + C \\
 \]
So, the sum of their present ages is 90 years.
Now, according to the data given in question, for 5 years ago
Sum of their ages will be $\left( {W - 5} \right) + \left( {C - 5} \right) = W + C - 10$
We have average = 20
Using formula for average, we get
 \[
  A = \dfrac{{W + C - 10}}{2} \\
\Rightarrow 20 = \dfrac{{W + C - 10}}{2} \\
\Rightarrow 20 \times 2 = W + C - 10 \\
\Rightarrow 40 + 10 = W + C \\
\Rightarrow 50 = W + C \\
 \]
So, the sum of wife and child present ages is 50 years.
Now, we need to calculate the present age of the husband.
Present age of husband = sum of husband, wife and child present ages – sum of wife and child present ages
Therefore, present age of husband = 90 – 50 = 40 years
Hence, option B is correct.

Note: Points to remember while solving age problems:-
1.If the present age is y, then n times the present age = ny.
2.If the present age is x, then age n years later/hence = x + n.
3.If the present age is x, then age n years ago = x – n.
4.The ages in a ratio a: b will be ax and bx.