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 the husband is :

Correct option is A

Given:

1. 3 years ago, the average age of husband, wife, and child was $27$ years.

   • Total age of husband, wife, and child 3 years ago:$$27\times 3=81\text{years}.$$

2. 5 years ago, the average age of the wife and the child was $20$ years.

   • Total age of wife and child 5 years ago:$$20\times 2=40\text{years}.$$

Step 1: Present Total Age of Wife and Child

• Their total age 5 years ago was $40$.
• Add $5$ years each for the wife and the child to calculate their current total age:$$40+5+5=50\text{years}.$$

Step 2: Present Total Age of Husband, Wife, and Child

• Their total age 3 years ago was $81$.
• Add $3$ years each for the husband, wife, and child to calculate their current total age:$$81+3+3+3=90\text{years}.$$

Step 3: Present Age of Husband

• Subtract the current total age of the wife and child from the current total age of all three :$$\text{Husband’s age}=90-50=40\text{years}.$$