Question : The average age of Ram and Shyam is 28 years. If Rahim replaces Ram, then the average age will become 26 years. If Rahim replaces Shyam, then the average age will become 30 years. What are the respective ages of Ram, Shyam, and Rahim?
Option 1: 32 years, 24 years, and 28 years
Option 2: 34 years, 40 years, and 30 years
Option 3: 48 years, 40 years, and 26 years
Option 4: 38 years, 44 years, and 36 years
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Correct Answer: 32 years, 24 years, and 28 years
Solution :
Average of Ram's and Shyam's age = 28
⇒ $\text{Ram + Shyam}=28\times2=56$
Average of Rahim's and Shyam's age = 26
⇒ $\text{Rahim + Shyam}=26\times2=52$
Average of Ram's and Rahim's age = 30
⇒ $\text{Ram + Rahim}=30\times2=60$
The sum of the ages = 56 + 52 + 60
⇒ 2(Ram + Rahim + Shyam) = 168
⇒ (Ram + Rahim + Shyam) = 84
Ram' age = (Ram + Rahim + Shyam) – ( Rahim + Shyam) = 84 – 52 = 32
Shyam' age = (Ram + Rahim + Shyam) – ( Rahim + Ram) = 84 – 60 = 24
Rahim' age = (Ram + Rahim + Shyam) – ( Ram + Shyam) = 84 – 56 = 28
Hence, the correct answer is 32 years, 24 years, and 28 years.
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