Question

28. Five years ago, the average age of four
men was 48 years. Now, a new man
joins and the average age increases by
2 years. What is the age of the new
man?​

Answer 1

$\bullet{\large \frak{QuEsTion}}\bullet$

Five years ago , the average age of four men was 48 years. Now , a new man joins and the average age increases by 2 years . What is the age of the new man ?

$\bullet {\large{\frak{SoluTion}}}\bullet$

Let, the present ages of four men be

a , b , c , d

such that

a+b+c+d = x

five years ago their ages will be

a - 5, b - 5, c - 5, d - 5

it is given that the average of their ages 5 years ago was 48 years

that is,

$\tt \frac{a-5+b-5+c-5+d-5}{4} = 48\\\\ \tt a+b+c+d - 20 = 192\\\\\tt x - 20 = 192\\\\\boxed {\tt x = 212 }$

Now,

let, present age of new man = y

it is given that when new man joins them the average increases by 2 years

that is ,

$\tt \frac{a+b+c+d+y}{5}=48+2\\ \\ \tt \frac{x+y}{5} = 50\\\\\tt x+y = 250\\\\\tt (putting\:value\:of x)\\\\\tt 212 + y = 250\\\\\boxed{\tt y = 250-212=38\:years}$

Therefore, the age of new man (present) is 38 years.