Question

(6) The ratio of Nisha and Nishant ages in 4:5. After 10 years the father's age will become 5:6. Find their
present ages .​

Answer 1

Step-by-step explanation:

let there present ages be 4x,5x

therefore after 8 years there ages will be 4x+8,5x+8

given 4x+8:5x+8=5:6

⇒6(4x+8)=5(5x+8)

therefore x=8

Answer 2

Their present ages :-

• The present age of Nisha = 40 years.
• The present age of Nishant = 50 years.

Given :

• The ratio of Nisha and Nishant ages = 4 : 5.
• After 10 years, the ratio of their ages = 5 : 6.

To Find :

• The present ages of Nisha and Nishant.

Solution :

We have to find the present age of Nisha and Nishant.

Let,

The age of Nisha be 4x.

The age of Nishant be 5x.

After 10 years,

The age of Nisha = 4x + 10

The age of Nishant = 5x + 10

First, we need to find the value of x.

According to the question,

After 10 years, the ratio of their ages will become 5 : 6.

That means,

$\bf \implies \dfrac{4x + 10}{5x + 10} = \dfrac{5}{6} \: \: \: .........(1)$

Now solve the equation (1) for finding the value of x.

$\bf \implies \dfrac{4x + 10}{5x + 10} = \dfrac{5}{6} \\ \\ \\ \bf \implies 5(5x + 10) = 6(4x + 10) \\ \\ \\ \bf \implies 25x + 50 = 24x + 60 \\ \\ \\ \bf \implies 25x - 24x = 60 - 50 \\ \\ \\ \bf \implies 1x = 10 \\ \\ \\ \bf \: \: \therefore \: \: \: x = 10$

Now, substitute the value of x in their ages.

★ The age of Nisha = 4x = 4 × 10 = 40 years.

★ The age of Nishant = 5x = 5 × 10 = 50 years.

Hence,

The present age of Nisha and Nishant is 40 years and 50 years.

Verification :

Substitute the value of 4x and 5x in the equation (1),

$\bf \implies \dfrac{4x + 10}{5x + 10} = \dfrac{5}{6}$

Where,

• The present age of Nisha (4x) = 40 years.
• The present age of Nishant (5x) = 50 years.

$\bf \implies \dfrac{40 + 10}{50 + 10} = \dfrac{5}{6} \\ \\ \\ \bf \implies \dfrac{50}{60} = \dfrac{5}{6} \\ \\ \\ \bf \implies \dfrac{5}{6} = \dfrac{5}{6}$

Hence Verified !