Question

Five years ago, the ratio of the ages of Rahul and
Sameer was 6:5. Five years later, Rahul will be
70 years old. What is Sameer's present age? ​

Answer 1

Let the present ages of

• Rahul be x
• Sameer be y

5 years ago;

• Rahul's age was (x - 5) years
• Sameer's age was (y - 5) years

According to the question,

$\sf{ \dfrac{x - 5}{y - 5} = \dfrac{6}{5} }$

$\dashrightarrow \: \sf{5(x - 5) = 6(y - 5)}$

$\to \: \sf{5x - 25 = 6y - 30}$

$\to \: \sf{5x - 6y + 5 = 0}$

$\to \: \sf{5x - 6y = - 5 \quad - - - (eqn.1)}$

Also, it is given that

Rahul will be 70 years old after 5 years.

→ x + 5 = 70

→ x = 70 - 5

→ x = 65 years.

Substitute the value of x in Equation 1 to find y

$\sf{5x - 6y = - 5}$

$\implies \sf{5(65) - 6y = - 5}$

$\implies \sf{325 - 6y = - 5}$

$\rightarrow \: \sf{ - 6y = - 330}$

$\rightarrow \: \sf{y = \dfrac{330}{6} }$

$\rightarrow \: \boxed{ \bf{y = 55}}$

Therefore

• Rahul's age = 65 years
• Sameer's age = 55 years

Answer 2

Question:

Five years ago, the ratio of the ages of Rahul and Sameer was 6:5. Five years later, Rahul will be 70 years old. What is Sameer's present age?

Solution:

Given:

• Ratio of the age of rahul and sameer = 6:5
• Age of rahul = x
• Age of sameer = y

After 5 years their age will be,

• Age of rahul after 5 years = x -5
• Age of sameer after 5 years = y - 5

Need to find:

• Age of rahul = ?
• Age of sameer = ?

Let's do it,

$\implies\sf{\frac{Age\:of\:rahul\:after\:5\:years}{Age\:of\:sameer\:after\:5\:years}}=\frac{ratio\:of\:the\:age\:of\:rahul}{ratio\:of\:the\:age\:of\:sameer}$

$\implies\sf{\frac{x-5}{y-5}=\frac{6}{5} }$

Cross multiplying the fractions,

$\implies\sf{5(x-5)=6(y-5)}$

$\implies\sf{5x-25=6y-30}$

$\implies\sf{5x-6y=-30+25}$

$\implies\sf{5x-6y=-5}$

$\:\:\:\:\:\:\:\:\:\:\:\:\to\sf{equation\:1}$

Now,5 years later rahul's age will be 70 years.

$\longrightarrow$ x + 5 = 70

$\longrightarrow$ x = 70 - 5

$\longrightarrow$ x = 65

• Here,x = 65.

Applying the value of x in equation 1,

5x - 6y = -5

5(65) - 6y = -5

325 - 6y = -5

$\sf{\cancel{-}6y = \cancel{-}330}\\ \\ \sf{6y=330}\\ \\ \sf{y=\frac{330}{6}}\\ \\ \sf{y=55}$

• Therefore,Rahul's age = 65 years and Sameer's age = 55 years.