If 3 times the mother's present age is 36 years more than 5 times her daughter's age, and 3 times the daughter's age is 4 years less than the mother's age, then what is the difference (in years) between the present ages of the mother and the daughter?

APEDIA

RRB NTPC Graduate Tier 1

2025 • 09 Jun, 2025 • Shift-1

If 3 times the mother's present age is 36 years more than 5 times her daughter's age, and 3 times the daughter's age is 4 years less than the mother's age, then what is the difference (in years) between the present ages of the mother and the daughter?

Correct Answer

Equation Formulation: Let the mother's present age be 'M' and the daughter's present age be 'D'. From the first condition, we derive: 3M = 5D + 36. From the sec......

💡 Analysis & Explanation

Equation Formulation ▼

Let the mother's present age be 'M' and the daughter's present age be 'D'. From the first condition, we derive: 3M = 5D + 36. From the second condition, we derive: 3D = M - 4, which simplifies to M = 3D + 4.

Solving for Variables ▼

Substitute the value of M into the first equation: 3(3D + 4) = 5D + 36. Expanding this yields 9D + 12 = 5D + 36. Rearranging terms gives 4D = 24, so D = 6. Using M = 3D + 4, we find M = 3(6) + 4 = 22.

Final Calculation ▼

The mother is 22 years old and the daughter is 6 years old. Their age difference is 22 - 6 = 16 years.

Conclusion ▼

The difference in their present ages is 16 years.

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If 3 times the mother's present age is 36 years more than 5 times her daughter's age, and 3 times the daughter's age is 4 years less than the mother's age, then what is the difference (in years) between the present ages of the mother and the daughter?