Question

The average age of $4$ persons five years ago was $45$ years. By including a fifth person, the present average age of all the five is $49$ years. The present age of the fifth person is

• A. $64$ years
• B. $48$ years
• C. $45$ years
• D. $40$ years

Answer 1

Answer: (C)

$45$ years

Let age of four persons at present be $x,y,z$ and $k$ respectively.

Five years ago,

Age of four persons be $x-5,y-5,z-5$ and $k-5.$

$\frac{x-5+y-5+z-5+k-5}{4}=45$

$\Rightarrow x+y+z+k-20=180$

$\Rightarrow x+y+z+k=200$ ...........................(i)

Let age of fifth person be $l.$

Now,

$\Rightarrow \frac{x+y+z+k+l}{5}=49$

$\Rightarrow 200+l=49\times 5$ (From eqn. i)

$\Rightarrow l=245-200$

$\Rightarrow l=45$ years.

Hence, C is the correct option.