Question

the ages of Nazia and Sana are in the ratio 5 ratio 7 4 years from now the ratio of their ages will be 3 ratio 4 their present ages are ​

Answer 1

Given :

• Ages of Nazia and Sana are in the ratio 5:7

• 4 years from now the ratio will be 3:4

To Find :

• Their present ages

Solution :

Let present age of Nazia be 5x and present age of Sana be 7x

After 4 years :

◆ Nazia's age = 5x + 4

◆ Sana's age = 7x + 4

According to the Question :

$\longrightarrow \sf \: \dfrac{5x + 4}{7x + 4} = \dfrac{3}{4}$

$\longrightarrow \sf \: 4(5x + 4) = 3(7x + 4)$

$\longrightarrow \sf \: 20x + 16 = 21x + 12$

$\longrightarrow \sf \: 20x - 21x = 12 - 16$

$\longrightarrow \sf \: - x = - 4$

$\longrightarrow \sf \red{ x = 4}$

We've assumed the Nazia's age as 5x and Sana's age be 7x. Let's find out their present ages by putting x = 4

$\bigstar \: \boxed{ \purple{ \sf \: Nazia's \: age = 5(4) = 20 \: years}}$

$\bigstar \: \boxed{ \purple{ \sf \: Sana's\: age = 7(4) =28 \: years}}$

Answer 2

AnswEr:-

Present ages of Nazia & Sana are 20 years & 28 years respectively.

$\rule{200}{1}$

To find:-

• Present ages of Nazia & Sana.

Solution:-

Case 1:-

• Ratio of present ages = 5 : 7

∴ Let the present ages of Nazia & Sana be 5y & 7y years respectively.

Case 2:-

• 4 years from now, ratio of ages will be 3 : 4

At first:-

4 years from now, their ages will be:

↠ Age of Nazia = (5y + 4) years.

↠ Age of Sana = (7y + 4) years.

Now according to question:-

⇒ (5y + 4) : (7y + 4) = 3 : 4

⇒ (5y + 4)/(7y + 4) = 3/4

After cross multiplication:-

⇒ 3(7y + 4) = 4(5y + 4)

⇒ 21y + 12 = 20y + 16

⇒ 21y - 20y = 16 - 12

⇒ y = 4

$\rule{200}{1}$

⋆ PRESENT AGES:-

⇒ Age of Nazia = 5y = 5(4) = 20 years.

⇒ Age of Sana = 7y = 7(4) = 28 years.

Therefore,

Present ages of Nazia & Sana are 20 years & 28 years respectively.