Question

Raju is 18 years younger than his cousin after 6 years their ages will be in the ratio 2:3 find their present ages​

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\green{Given}}}}}$

• Raju is 18 years younger than his Cousin
• after 6 years their ages will be in the ratio 2:3

$\bf{\underline{\underline{\sf{\green{To\:find}}}}}$

• Present age of Raju
• Present age of cousin

$\bf{\underline{\underline{\sf{\green{Solution}}}}}$

Let the present age of Raju be x years.

Let the present age of cousin be y years.

$\bf{\underline{\underline{\sf{\blue{As\:per\:first\:condition}}}}}$

• Raju is 18 years younger than his cousin

Representing the condition mathematically.

=> x = y - 18

=> x - y = - 18 ----> 1

$\bf{\underline{\underline{\sf{\blue{As\:per\:second\:condition}}}}}$

• After 6 years their ages will be in the ratio 2:3

Ages after 6 years :-

Farhan = x + 6 years

Cosin = y + 6 years

Representing the condition mathematically.

=> $\large\frac{x\:+\:6}{y\:+\:6}$ = $\large\frac{2}{3}$

Cross multiplying,

=> 3 ( x + 6) = 2 ( y + 6)

=> 3x + 18 = 2y + 12

=> 3x - 2y = 12 - 18

=> 3x - 2y = - 6 ----> 2

Multiply equation 1 by 2,

=> x - y = - 18

=> 2 × x - 2 × y = 2 × - 18

=> 2x - 2y = - 36 ----> 3

Solve equation 2 and equation 3 simultaneously by elimination method.

Subtract equation 3 from equation 2,

...+ 2x - 2y = - 36 -----> 3

- (+ 3x - 2y = - 6 ) -----> 2

-------------------------------

- x = - 30

x = 30

Substitute x = 30 in equation 3,

=> 2x - 2y = - 36

=> 2 ( 30) - 2y = - 36

=> 60 - 2y = - 36

=> - 2y = - 36 - 60

=> - 2y = - 96

=> y = $\large\frac{-96}{-2}$

=> y = $\large\frac{96}{2}$

=> y = 48

$\bf{\large{\underline{\boxed{\sf{\pink{Present\:age\:of\:Raju\:=\:x\:=\:30\:years}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\pink{Present\:age\:of\:cousin\:=\:y\:=\:48\:years}}}}}}$

$\bf\large\underline{Verification:}$

For first case :-

• Raju is 18 years younger than his Cousin

Present age of Raju = 30 years

Present age of Cousin = 48 years

=> x = y - 18

=> 30 = 48 - 18

=> 30 = 30

LHS = RHS.

For second case :-

• After 6 years their ages will be in the ratio 2:3

Ages after 6 years :-

Farhan = x + 6 = 30 + 6 = 36 years

Cousin = y + 6 = 48 + 6 = 54 years

=> $\large\frac{x+6}{y+6}$ = $\large\frac{2}{3}$

$\large\frac{36}{54}$ = $\large\frac{2}{3}$

Dividing LHS by 18,

=> $\large\frac{2}{3}$ = $\large\frac{2}{3}$

LHS = RHS.

Hence verified.

Answer 2

Answer:

here your answer..............

Step-by-step explanation:

let the present age of Raju be x year's

then his cousin age was x+18.

And

after 6 year's Raju and his cousin

ages x+6 and x+24

According to question

x+6:x+24=2:3

x+6/x+24=2/3

3(x+6)=2(x+24)

3x+18=2x+48

3x-2x=48-18

x=30

therefore the present age of Raju

is x=30 years

and his cousin age is

x+18=30+18=48 year's.