Question

If 1added to each of the two numbers then they are in the ratio 1:2. If 5 is subtracted from each of the two numbers then the ratio becomes 5:11.Find the numbers.

Answer 1

Dear Student,

Let the two numbers be x and y.

Case 1:

According to the given condition, $\frac{x+1}{y+1}=\frac{1}{2}$

⇒ 2x + 2 = y + 1

⇒ 2x - y = - 1 .... (1)

Case 2:

Again, according to the given condition, $\frac{x-5}{y-5}=\frac{5}{11}$

⇒ 11x - 55 = 5y - 25

⇒ 11x - 5y = 30 .... (2)

Now multiply equation (1) by 5 subtract it from (2), we get

⇒ 11x - 5y -(10x - 5y) = 30 -(-5)

⇒ 11x - 5y -10x + 5y = 30 + 5

⇒ x = 35

On putting the value of x in (1), we get

2(35) - y = -1

⇒ -y = -1 - 70

⇒ y = 71

Regards