Question

Ajay and Raj together have Rs.1050.On taking 150 from Ajay,
Ajay will have same Amount as what Raj had earlier. Find the
ratio of amount with Ajay and Raj initially?​

Answer 1

$\Large{\underline{\underline{\bf{AnSweR:-}}}}$

4 : 3

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

◈ Let the money with Ajay be denoted as 'x' and that of Raj be denoted as 'y'.

Now

◈ According to the question,

❥ x + y = Rs. 1050   ...( 1 )

After 150 rupees is taken from Ajay, Ajay would have the same money which Raj had. Hence interpreting it as an equation we get,

❥ x - 150 = y   ...( 2 )

◈━━━━━━━ ⸙ ━━━━━━━ ◈

Substituting ( 2 ) in ( 1 ) we get,

❥ x + x - 150 = 1050

❥ 2x = 1050 + 150

❥ 2x = 1200

❥ x = 1200 / 2 = 600

Hence Ajay had Rs. 600 initially.

❥ y = x - 150

❥ y = 600 - 150

❥ y = Rs. 450

◈ Hence Raj had 450 initially.

◈ Ratio of Ajay's Money to Raj's Money is:

❥ x : y = 600 : 450 = 4 : 3

Hence 4 : 3 is the required ratio.

◈ ━━━━━━━ ⸙ ━━━━━━━ ◈

Answer 2

Answer :

›»› The ratio of amount with Ajay and Raj initially is 4:3

Given :

• Ajay and Raj together have Rs.1050.On taking 150 from Ajay, Ajay will have same Amount as what Raj had earlier.

To Find :

• The ratio of amount with Ajay and Raj initially.

How to Find?

❒ Here in this question we have to find The ratio of amount with Ajay and Raj initially. So, firstly we have to assume the money with Ajay as a variable and accordingly to Raj, after that we will find The ratio of amount with Ajay and Raj initially on the basis of conditions given above$.$

Required Solution :

Let ,

The money with Ajay be "x" and Raj be "y"

x + y .....1

x - 150 = y .....2

Substitute equation (2) in equation (1)

⇒ x + x - 150 = 1050

Calculate between similar terms,

⇒ 2x - 150 = 1050

Move the constant to the right side and change the sign,

⇒ 2x = 1050 + 150

Add 1050 and 150,

⇒ 2x = 1200

Divide both sides by the same number,

⇒ x = 600

Put the value of x in equation (2)

⇒ 600 - 150 = y

Subtract 600 from 150,

⇒ 450 = y

⇒ y = 450

Therefore ,

• Money with Ajay = x = 600
• Money with Raj = y = 450

Now ,

⇛ Ratio = x/y

⇛ Ratio = 600/450

⇛ Ratio = 4/3

⇛ Ratio = 4:3

║Hence, the ratio of amount with Ajay and Raj initially is 4:3.║