Question

8. The ages of two brothers differ by 24 years. If
six years ago the elder brother was three times as
old as the younger one, then find the present age of
the elder brother.
(1) 42 years
(2) 24 years
(3) 36 years
(4) 28 years
(5) None of these​

Answer 1

Answer :-

Option (1) 42 years

$\rule{150}2$

Let the -

• present age of one brother be x years
• present age of another brother be y years

The ages of two brothers differ by 24 years.

=> $\sf{x\:-\:y\:=\:24}$

=> $\sf{x\:=\:24\:+\:y}$ ....(1)

Six years ago the elder brother was three times as

old as the younger one.

Let the -

• the present age of elder brother be x years
• present age of younger brother be y years

$\bold{\sf{6\:years\:ago} \begin{cases} \text{Age of elder brother = (x-6) years} \\ \text{Age of younger brother = (y-6) years} \end{cases}}$

According to question,

=> $\sf{x\:-\:6\:=\:3(y\:-\:6)}$

=> $\sf{x\:-\:6\:=\:3y\:-\:18}$

=> $\sf{x\:-\:3y\:=\:-\:18\:+\:6}$

=> $\sf{24\:+\:y\:-\:3y\:=\:-\:12}$ [From (1)]

=> $\sf{-2y\:=\:-36}$

=> $\sf{y\:=\:18}$

Substitute value of y = 5 in (1)

=> $\sf{x\:=\:24\:+\:18}$

=> $\sf{x\:=\:42}$

•°• Present age of elder brother = x = 42 years

Present age of younger brother = y = 18 years

Answer 2

$\huge\tt {Answer}$

42 is the present age of elder brother.

Option (1)

Step-by-step explanation:

Let M be the present age of one brother and let N be the preset age of another brother.

24 is the age difference between two brothers.

$M - N = 24 \\ M = 24 + N \: \: - eq(1)$

Let M be the age of elder brother and N be the age of younger brother.

6 years their ages are

-> Elder brother = ( M - 6 ) years

-> Younger brother = ( N - 6 ) years

According to question:

$= M- 6 = 3(N - 6) \\ = M - 6 = 3N - 18 \\ = M - 3N = - 18 + 6 \\ = 24 + N - 3N = - 12 \\ = - 2N = - 36 \\ = N = 18$

Substuting ( y = 5 ) for Eq(1)

$= M = 24 + 18 \\ = N = 42$

Hence, 42 is the present age of elder brother and also , 18 is the present age of younger brother.