Question : The average age of Rustam and Preetam is 39 years. The average age of Preetam and Geetam is 28 years. The average age of Rustam and Geetam is 34 years. What will be the age (in years) of the youngest of the three after 10 years?
Option 1: 13
Option 2: 23
Option 3: 33
Option 4: 43
Correct Answer: 33
Solution :
Let the ages of Rustam, Preetam, and Geetam be $r,p,$ and $g,$ respectively.
Given: $\frac{r + p}{2} = 39$
⇒ $r + p = 78$
⇒ $p = 78-r$ ...........(1)
And $\frac{p + g}{2} = 28$
⇒ $p + g = 56$ ...........(2)
Also, $\frac{r + g}{2} = 34$
⇒ $r + g = 68$
⇒ $g = 68-r$ ............(3)
Substituting the value of p and g in terms of r from (1) and (3) in (2):
⇒ $78 - r + 68 - r = 56$
⇒ $146 - 2r = 56$
⇒ $2r = 90$
$\therefore r = 45$
So, $p = 78 - 45 = 33$ and $g = 68 - 45 = 23$
$\therefore$ The youngest is Geetam with the age of 23 years.
⇒ Geetam’s age after 10 years = 23 + 10 = 33 years
Hence, the correct answer is 33.
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