Question

Navin is 4 years elder to Ajay . After 10 years , the ratio of the ages of Navin and Ajay is 10 : 9 Find Ajay's present age .

Answer 1

⠀⠀ ☯ Let's consider that the present age of Ajay be x.

And, Navin is 4 years elder to Ajay.

⠀⠀⠀

$:\implies\sf Navin = (x + 4)$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀

⠀$\large\sf\underline{\bigstar\; According \ to \ Question\;:}$

⠀⠀⠀⠀After 10 years, the ratio of the ages of Navin and Ajay is 10 : 9.

⠀⠀⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀⠀⠀

$:\implies\sf \dfrac{(x + 4) + 10}{x + 10} = \dfrac{10}{9} \\\\\\:\implies\sf (x + 14)9 = 10x + 100 \\\\\\:\implies\sf 9x + 126 = 10x + 100\\\\\\:\implies\sf 126 - 100 = 10x - 9x\\\\\\:\implies{\boxed{\boxed{\frak{\pink{x = 26}}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀

Now,

• Ajay's age, x = 26
• Navin's age, (x + 4) = 26 + 4 = 30

⠀⠀⠀⠀⠀⠀

$\therefore\:{\underline{\sf{Present \ Age \ of \ Ajay \ is \ {\textsf{\textbf{26 years.}}}.}}}$⠀⠀⠀

Answer 2

Answer:

Given :-

• Navin is 4 years elder to Ajay. After 10 years the ratio of the ages of Navin and Ajay is 10 : 9.

To Find :-

• What is the present age of Ajay.

Solution :-

Let, the present age of Ajay be x

And, the present age of Navin be x + 4

After 10 years,

Age of Ajay be x + 10

And, the age of Navin will be 10 + (x + 4)

According to the question,

↦ $\sf\dfrac{10 + (x + 4)}{x + 10} =\: \dfrac{10}{9}$

↦ $\sf\dfrac{x + 14}{x + 10} =\: \dfrac{10}{9}$

By doing cross multiplication we get,

↦ 9(x + 14) = 10(x + 10)

↦ 9x + 126 = 10x + 100

↦ 9x - 10x = 100 - 126

↦ - x = - 26

➠ x = 26

Hence, their required present ages will be,

✧ Present age of Ajay = x = 26 years

✧ Present age of Navin = x + 4 = 26 + 4 = 30 years

$\therefore$ The present age of Ajay is 26 years .

✪ Let's Verify :-

⇒ $\sf\dfrac{10 + (x + 4)}{x + 10} =\: \dfrac{10}{9}$

⇒ $\sf\dfrac{x + 14}{x + 10} =\: \dfrac{10}{9}$

Put x = 26 we get,

⇒ $\sf\dfrac{26 + 14}{26 + 10} =\: \dfrac{10}{9}$

By doing cross multiplication we get,

⇒ 9(26 + 14) = 10(26 + 10)

⇒ 9(40) = 10(36)

⇒ 360 = 360

➦ LHS= RHS

Hence, Verified ✔