Question

Ten years back, Suresh and Ramesh's ages were in proportion of 2 : 5. After
6 years, this proportion will be 2 : 3. What is Suresh's age today?​

Answer 1

Answer:

• Suresh's present age is 18 years

Step-by-step explanation:

Given that:

• Ten years back, Suresh and Ramesh's ages were in proportion of 2 : 5.
• After 6 years, this proportion will be 2 : 3.

To Find:

• Suresh's present age.

Let us assume:

• Suresh's age 10 years ago be 2x.

Then,

• Ramesh's age 10 years ago will be 5x.

Present time (10 years later):

• Suresh's age = 2x + 10
• Ramesh's age = 5x + 10

6 years after present time:

• Suresh's age = 2x + 10 + 6 = 2x + 16
• Ramesh's age = 5x + 10 + 6 = 5x + 16

According to the question:

$\sf{\dfrac{2x+16}{5x+16}=\dfrac{2}{3}}$

By cross-multiplication,

$\sf{\longrightarrow 2(5x+16)=3(2x+16)}$

Opening the brackets,

$\sf{\longrightarrow 10x+32=6x+48}$

Transposing variables to LHS and constants to RHS and changing their sign,

$\sf{\longrightarrow 10x-6x=48-32}\\\\\longrightarrow 4x = 16$

Transposing 4 from LHS to RHS and changing its sign,

$\sf{\longrightarrow x = \dfrac{16}{4}}$

Dividing 16 by 4,

$\sf{\longrightarrow x = 4}$

Hence, x = 4.

Therefore,

• Suresh's age 10 years ago = 2x = 8.
• Suresh's present age = 2x + 10 = 8 + 10 = 18

Hence, Suresh's present age is 18 years.