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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


Team Careers360 21st Jan, 2024
Answer (1)
Team Careers360 22nd Jan, 2024

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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