The sum of the present ages of a father and his son is 18 years more than 4 times the present age of the son. After 5 years, 4 times the father's age will be 8 years less than 14 times the son's age. The difference (in years) between the present ages of the father and the son is:

APEDIA

NTPC Graduate Tier 1

2025 • 06 Jun, 2025 • Shift-2

The sum of the present ages of a father and his son is 18 years more than 4 times the present age of the son. After 5 years, 4 times the father's age will be 8 years less than 14 times the son's age. The difference (in years) between the present ages of the father and the son is:

Correct Answer

Initial Equation Setup: Let the father's present age be F and the son's be S. The first condition translates to: F + S = 4S + 18. Simplifying this yields F - 3S......

💡 Analysis & Explanation

Initial Equation Setup ▼

Let the father's present age be F and the son's be S. The first condition translates to: F + S = 4S + 18. Simplifying this yields F - 3S = 18.

Future Age Condition ▼

In 5 years, their ages will be (F + 5) and (S + 5). The second condition is: 4(F + 5) = 14(S + 5) - 8. Expanding this gives 4F + 20 = 14S + 70 - 8, which simplifies to 4F - 14S = 42, or further down to 2F - 7S = 21.

Solving the System ▼

Multiply the first simplified equation by 2 to get 2F - 6S = 36. Subtracting the second equation (2F - 7S = 21) from this gives S = 15. Substituting S = 15 back into F - 3(15) = 18 results in F = 63.

Final Calculation ▼

The difference between their present ages is F - S = 63 - 15 = 48 years.

Conclusion ▼

The exact age difference is 48 years.

Choose Language

See you soon!

The sum of the present ages of a father and his son is 18 years more than 4 times the present age of the son. After 5 years, 4 times the father's age will be 8 years less than 14 times the son's age. The difference (in years) between the present ages of the father and the son is: