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?
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A32 yr
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B40 yr
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C36 yr
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DCannot be determined
Answer
Correct Answer: 32 yr
Explanation
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:
3(8x + 8) = 10(x + 8)24x + 24 = 10x + 80 ⇒ 14x = 56 ⇒ x = 4Meena now = 8x = 32Verification / 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