Question

The ages of Amaan and Farhaan are in the ratio 8:7.Six years later. Their ages will be in the ratio 10:9.Find the ratio.

Answer 1

Given :

• The ages of Amaan and Farhaan are in the ratio 8:7.

• Six years later their ages will be in the ratio 10:9.

To find :

• The ratio of their present ages = ?

Step-by-step explanation :

Let, the ratio of the Aman's age be 8x.

Then, the ratio of the Farhaan's age be 7x.

Six years later Aman's age = 8x + 6

Six years later Farhaan's age = 7x + 6

According to the question :

➮ 8x + 6 / 7x + 6 = 10/9

➮ 9(8x + 6) = 10(7x + 6)

➮ 72x + 54 = 70x + 60

➮ 72x - 70x = 60 - 54

➮ 2x = 6

➮ x = 6/2

➮ x = 3.

Therefore, We get the value of x = 3.

Hence,

Aman's present age = 8x = 8 × 3 = 24 year's

Farhaan's present age = 7x = 7 × 3 = 21 year's

Now,

Ratio of their ages = Aman's age : Farhaan's age

So, we get,

Ratio = 24 : 21

In the simplest form we get, 24/21 = 8/7.

Answer 2

Answer:

Let the Present Age be 8n and 7n of Amaan and Farhaan respectively.

$\underline{\bigstar\:\textsf{Six Years Later, ATQ :}}$

$:\implies\sf \dfrac{Amaan+6}{Farhaan+6}=\dfrac{10}{9}\\\\\\:\implies\sf \dfrac{8n + 6}{7n + 6} = \dfrac{10}{9}\\\\\\:\implies\sf (8n + 6) \times 9 = 10 \times (7n + 6)\\\\\\:\implies\sf 72n + 54 = 70n + 60\\\\\\:\implies\sf 72n - 70n = 60 - 54\\\\\\:\implies\sf 2n = 6\\\\\\:\implies\sf n = \dfrac{6}{2}\\\\\\:\implies\sf n = 3$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{Present Ages :}}$

$\bullet\:\:\textsf{Amaan = 8n = 8(3) = \textbf{24 years}}\\\bullet\:\:\textsf{Farhaan = 7n = 7(3) = \textbf{21 years}}$