Question : The average age of Rustam and Preetam is 30 years. The average age of Preetam and Geetam is 20 years. The average age of Rustam and Geetam is 26 years. What will be the age of the youngest of the three after 5 years?
Option 1: 21 years
Option 2: 22 years
Option 3: 26 years
Option 4: 25 years
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Correct Answer: 21 years
Solution :
The average age of Rustam and Preetam = 30 years
Use the formula to find the average, Average = $\frac{\text{Sum of the ages}}{{\text{Total number of Person}}}$
The sum of their ages = Average × Total number of Person = 2 × 30 = 60 years
The average age of Preetam and Geetam = 20 years = 2 × 20 = 40 years
The average age of Rustam and Geetam = 26 years = 2 × 26 = 52 years
So, Sum of the ages of three = 60 + 40 + 52 = 152
⇒ 2(Rustam +Preetam + Geetam) = 152
⇒ (Rustam +Preetam + Geetam) = 76
Age of Geetam (youngest one) = 76 – Sum of the age of Rustam and Preetam = 76 – 60 = 16
After 5 years, she will be 16 + 5 = 21 years old
Hence, the correct answer is 21 years.
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