Question

If two is added to each of two given numbers, the ratio becomes 1:2. however if 4is subtracted from each of the given numbers, the ratio becomes 5:11. find the numbers?

Answer 1

(x+2)/(y+2)= 1/2
(x-4)/(y-4)= 5/11
on simplification we got two equations
11x-5y=24
2x-y=-2
on solving
x = 34
y = 70

Answer 2

Answer:

Step-by-step explanation:

Given :-

Two is added to each of two given numbers, the ratio becomes 1:2.

4 is subtracted from each of the given numbers, the ratio becomes 5:11.

To Find :-

The Numbers,

Solution :-

Let the numbers be x and y.

According to Question.

1st Equation

⇒ x+2/ y+2 = 1/2  

By cross multiplication

⇒ 2(x + 2) = y + 2  

⇒ 2x + 4 = y + 2  

⇒ 2x – y = -2 ……(i)  

2nd Equation.

⇒ x−4/ y−4 = 5/11  

By cross multiplication

⇒ 11(x−4) = 5(y−4)

⇒ 11x – 44 = 5y – 20  

⇒11x – 5y = 24 ……(ii)  

On multiplying eq (i) by 5

10x – 5y = -10  

On subtracting (iii) from (ii),

⇒ x = (24 + 10)

⇒ x = 34  

Putting x value in eq (i)

⇒ 2x – y = -2

⇒ 2 × 34 – y = -2  

⇒ 68 – y = -2  

⇒ y = (68 + 2)

⇒ y = 70  

Hence, the numbers are 34 and 70.