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

EXPLANATION.

• GIVEN

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 present age.

According to the question,

Let the present age of rahul be = x years.

Let the present age of sameer be = y years.

Case = 1

Five years ago, the ratio of the ages of rahul

and sameer was = 6:5

=> x - 5 / y - 5 = 6/5

=> 5 ( x - 5 ) = 6 ( y - 5 )

=> 5x - 25 = 6y - 30

=> 5x - 6y = -5 ......(1)

Case = 2

Five years later,rahul will be 70 years old.

=> x + 5 = 70

=> x = 65

put the value of x = 65 in equation (1)

we get,

=> 5 ( 65 ) - 6y = -5

=> 325 - 6y = -5

=> -6y = -5 - 325

=> -6y = -330

=> y = 55

Therefore,

Age of rahul = 65 years.

Age of sameer = 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.