Question

The present ages of Ram and Mohan are in the ratio 11:8 . Eight years later

the sum of their ages will be 54 years . What are their present ages?​

Answer 1

Given:

We have been given the ratio of present of ages of Ram and Mohan .

• Present age are in Ratio 11:8
• Eight years later , sum of their ages will be 54 years

Solution:

We have to find the Present ages of Ram and Mohan by using given data

• Let , Present age of Ram = x
• Present age of Mohan = y

We have to make two pair of linear Equation using the above assumed variables. These Equation can be solved further by using any of the following method :

• Substitution Method
• Elimination Method
• Cross Multiplication Method

$\sf{}$

According to first condition:

The ratio of present ages of Ram and Mohan is 11:8

$\because{ \boxed{ \rm{\dfrac{Ram \: age}{Mohan \: age}= \dfrac{11}{8} }}}$

Substituting the assumed values in Equation:

$\longrightarrow \sf{ \dfrac{x}{y} = \dfrac{11}{8}}$

Cross Multiplying the Equation

$\longrightarrow \sf{8x = 11y}$

$\longrightarrow \sf{8x - 11y = 0 }$ ----------(1)

$\sf{}$

According to second condition:

Eight years later , age will be

• Age of Ram = x + 8
• Age of Mohan = y + 8

Sum of ages of Ram and Mohan is 54 years

$\because{ \boxed{ \rm{Sum \: of \: ages = 54 }}}$

$\longrightarrow \sf{ ( x + 8 ) + ( y + 8 ) = 54}$

$\longrightarrow \sf{ x + y + 16 = 54}$

$\longrightarrow \sf{ x + y = 38 }$ ------(2)

$\sf{}$

Solving pair of linear Equation

Multiplying by 11 in Equation (2) and then adding the modified equation with Equation (1)

$\longrightarrow \sf{ 11x + 11y + 8x - 11y = 418}$

$\longrightarrow \sf{ 11x + \cancel{11y} + 8x - \cancel{11y} = 418}$

$\longrightarrow \sf{ 19x = 418}$

$\longrightarrow \sf{ x = \dfrac{418}{19}}$

$\longrightarrow \sf{ x = 22 }$

Putting value of x in Equation (1) we get

$\longrightarrow \sf{ y = 16 }$

$\sf{}$

$\large{\therefore{\underline{\boxed{\bf{\blue{Ram \: age = 22 years}}}}}}$

$\large{\therefore{\underline{\boxed{\bf{\blue{Mohan \: age = 16 years}}}}}}$

Answer 2

Given :

• Present age of Ram and Mohan in ratio = 11 : 8

• 8 years later, sum of their ages = 54 years

To find :

• Present ages of Ram and Mohan

According to the question :

Let the age of Ram be ' 11x '

Mohan's age be ' 8x '

8 years later,

Ram's age will be = 11x + 8

Mohan's age will be = 8x + 8

Equation will be :

⟹ ( 11x + 8 ) + ( 8x + 8 ) = 54

⟹ ( 11x + 8x ) + ( 8 + 8 ) = 54

⟹ 19x + 16 = 54

⟹ 19x = 54 / 16

⟹ 19x = 38

⟹ x = 38 / 19

⟹ x = 2

To find :

Their present ages,

➳ Ram = 11x = 11 × 2 = 22 years

➳ Mohan = 8x = 8 × 2 = 16 years

So, It's Done !!