Question

The ratio of two numbers is 5 ∶ 4. A number y is then subtracted from each of the two given numbers so that the ratio of the resultant numbers becomes 2 ∶ 1. What would be the ratio of the resultant numbers when the same number y is added to each of the two initial numbers?

• A. 3 : 2
• B. 5 : 4
• C. 7 : 6
• D. 8 : 7

Answer 1

Answer:

D. 8 : 7

Given:

Initial ratio of two numbers is 5 : 4

y is subtracted from each of the two numbers then the ratio becomes 2 : 1 

Calculation:

Let the two numbers be 5x and 4x.

According to the question,

$\frac{(5x - y)}{(4x - y)}=\frac{2}{1}$

⇒ 5x - y = 8x - 2y

⇒ 3x = y     -----(1)

Now, The ratio when y is added to the two numbers,

⇒ (5x + y) : (4x + y)

Take the value of y from equation (1), we get

⇒ (5x + 3x) : (4x + 3x)

⇒ 8x : 7x

⇒ 8 : 7

∴ The ratio of the two numbers when y added to them is 8 : 7