Join 60,000+ competitive exam aspirants
The sum of ages of Raj and Ravi is 8 years more than the sum of ages of Ravi and Rahul. How many years older is Raj as compared to Rahul?
4 years
8 years
12 years
16 years
8 years
Since the common person (Ravi) appears on both sides of the equation, cancel his age directly. The difference between the remaining individuals (Raj and Rahul) must equal the given surplus of 8 years.
Sum of ages of Raj and Ravi is 8 years more than the sum of ages of Ravi and Rahul.
(RaтАЛ+RvтАЛ)=(RvтАЛ+RlтАЛ)+8
Since the common person (Ravi) appears on both sides of the equation, cancel his age directly. The difference between the remaining individuals (Raj and Rahul) must equal the given surplus of 8 years.
Students often try to assign arbitrary ages to Ravi (e.g., setting Ravi's age to 20), which is unnecessary and time-consuming; the variable RvтАЛ is irrelevant as it cancels out.
Set up the algebraic equation
Let the ages of Raj, Ravi, and Rahul be RaтАЛ, RvтАЛ, and RlтАЛ respectively. Based on the problem statement, we write the equation.
RaтАЛ+RvтАЛ=RvтАЛ+RlтАЛ+8
Simplify the equation
Subtract the age of Ravi (RvтАЛ) from both sides of the equation to isolate the relationship between Raj and Rahul.
RaтАЛ=RlтАЛ+8
Find the difference
Rearrange the equation to find how many years older Raj is compared to Rahul (RaтАЛтИТRlтАЛ).
RaтАЛтИТRlтАЛ=8
B is correct because the cancellation of Ravi's age in the equation RaтАЛ+RvтАЛ=RvтАЛ+RlтАЛ+8 leaves RaтАЛ=RlтАЛ+8, showing Raj is 8 years older than Rahul.
This logic is identical to balance-scale problems in Physics or accounting reconciliation, where common terms on both sides of an equality cancel out.