Pushpa is twice as old as Rita was two years ago. If the difference between their present ages is 2 years, how old is Pushpa today?
Verbal Reasoning
Problems on Ages
Difficulty: Easy
Choose an option
-
A6 years
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B8 years
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C10 years
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D12 years
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ENone of these
Answer
Correct Answer: 8 years
Explanation
Introduction / Context:This problem mixes a “twice as old as” condition referring to the past with a present-age difference. We form two equations in two unknowns.
Given Data / Assumptions:
- Let Pushpa = P, Rita = R (present ages).
- P = 2(R − 2)
- P − R = 2
Concept / Approach:Direct substitution is simplest: solve the two simultaneous linear equations to obtain integer ages.
Step-by-Step Solution:
From P − R = 2 ⇒ P = R + 2Set R + 2 = 2(R − 2)R + 2 = 2R − 4 ⇒ 6 = R ⇒ R = 6Thus P = R + 2 = 8Verification / Alternative check:
Two years ago: Rita = 4, twice that is 8 ⇒ Pushpa = 8 ✓Why Other Options Are Wrong:
- 6 years is Rita's present age, not Pushpa's.
- 10 and 12 do not satisfy both conditions simultaneously.
- None of these: 8 works perfectly.
Common Pitfalls:Applying “twice as old” to the present age of Rita rather than her age two years ago; or assuming the older person is not specified by the difference (here, difference confirms who is older).
Final Answer:8 years