Six years ago, the ratio of the ages of the two persons P and Q was 3:2. Four years hence the ratio of their ages will be 8:7. What is P's age?

10 years

12 years

14 years

8 years

APEDIA

NTPC Graduate Tier 1

2016 • 02 Apr, 2016 • Shift 2

Six years ago, the ratio of the ages of the two persons P and Q was 3:2. Four years hence the ratio of their ages will be 8:7. What is P's age?

Correct Answer

12 years

Timeline Variables: Let the precise ages of P and Q exactly six years ago be algebraically represented as 3x and 2x respectively. Their mathematical present age......

💡 Analysis & Explanation

Timeline Variables ▼

Let the precise ages of P and Q exactly six years ago be algebraically represented as 3x and 2x respectively. Their mathematical present ages directly translate to (3x + 6) and (2x + 6).

Future Condition Setup ▼

Exactly four years progressively from the present, their combined timeline ages will effectively be (3x + 6 + 4) and (2x + 6 + 4), easily simplifying to (3x + 10) and (2x + 10). The strictly given ratio at this future point is firmly 8:7.

Equation Solving ▼

Creating the fraction (3x + 10) / (2x + 10) = 8 / 7. Cross-multiplying strictly gives 21x + 70 = 16x + 80. Rearranging terms properly leaves 5x = 10, meaning x perfectly equals 2.

Final Calculation ▼

P's present baseline age is established as 3x + 6. Substituting x = 2 gives 3(2) + 6 = 12.

Conclusion ▼

P's exact current age is definitively 12 years.

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Six years ago, the ratio of the ages of the two persons P and Q was 3:2. Four years hence the ratio of their ages will be 8:7. What is P's age?