Mother–daughter present ages from future ratio: Meena is currently 8 times her daughter’s age. In 8 years, their ages will be in the ratio 10 : 3. What is Meena’s present age?

Introduction / Context:
Two conditions—one multiplicative now, one ratio in the future—allow direct solution. Assign the daughter’s current age a variable and solve from the future ratio to find both ages.

Given Data / Assumptions:

• Meena now = 8x, Daughter now = x
• (8x + 8) : (x + 8) = 10 : 3

Concept / Approach:
Cross-multiply the future ratio and solve for x. Then compute Meena’s present age 8x.

Step-by-Step Solution:

Verification / Alternative check:
In 8 years: Meena = 40, Daughter = 12 ⇒ 40 : 12 = 10 : 3 ✓.

Why Other Options Are Wrong:
40 and 36 are not Meena’s present age under the given constraints. “Cannot be determined” is false since the system is determinate.

Common Pitfalls:
Switching which age is multiplied by 8; forgetting both increase by 8 years in the future ratio.

Final Answer:
32 yr