Grandfather–grandson relation via division: If (Randheer’s present age − 6) divided by 18 gives his grandson Anup’s present age. Anup is 2 years younger than Mahesh, whose age is 5 years. Find Randheer’s age.
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A96 years
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B84 years
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C48 years
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D60 years
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ENone of these
Answer
Correct Answer: 60 years
Explanation
Introduction / Context:This is a direct algebraic translation of a sentence involving subtraction and division. The key is to determine Anup’s age from Mahesh’s and then back-solve for Randheer, ensuring the arithmetic order (subtract then divide) is preserved.
Given Data / Assumptions:
- Mahesh = 5 years.
- Anup is 2 years younger ⇒ Anup = 3 years.
- (Randheer − 6) / 18 = Anup.
Concept / Approach:Compute Anup first, then treat the given as a linear equation in R. Multiplying both sides by 18 after substituting Anup gives Randheer's age explicitly.
Step-by-Step Solution:
Anup = 3(R − 6)/18 = 3 ⇒ R − 6 = 54 ⇒ R = 60Verification / Alternative check:Check: (60 − 6) / 18 = 54/18 = 3 years, which matches Anup.
Why Other Options Are Wrong:96/84/48 are incompatible with the linear relation after plugging Anup = 3.
Common Pitfalls:Dividing first or misreading the phrase as 18/(R − 6); the statement clearly means subtract then divide.
Final Answer:60 years