Question : Directions: The sum of Kartik and his parents' ages is 122 years. Kartik's age is half of his mother's age. His mother is 7 years younger than his father. What is Kartik's age (in years) at present?
Option 1: 23
Option 2: 15
Option 3: 26
Option 4: 20
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Correct Answer: 23
Solution :
Given:
Let the age of Kartik = k
The age of his father = x
And the age of his mother = y
The sum of Kartik and his parents' ages is 122 years→k + x + y = 122
Kartik's age is half of his mother's age→k = y ÷ 2; y = 2k
Kartik's mother is 7 years younger than his father→ x = y – 7; 2k – 7
Now, substituting values of x and y in terms of k in equation (I), we have –
k + 2k – 7 + 2k = 122
5k – 7 = 122
5k = 115
k = 23
So, the age of Kartik is 23 years. Hence, the first option is correct.
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