Question

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

Answer 1

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Answer 2

Let the two numbers be x and y.

Given that if 2 is added to each of two given numbers their ratio becomes 1:2.

$= > \frac{x + 2}{y + 2} = \frac{1}{2}$

= > 2(x + 2) = y + 2

= > 2x + 4 = y + 2

= > 2x - y = -2 --------- (1)

Given that if 4 is subtracted from each of the given numbers the ratio will be 5:11.

$= > \frac{x - 4}{y - 4} = \frac{5}{11}$

= > 11(x - 4) = 5(y - 4)

= > 11x - 44 = 5y - 20

= > 11x - 5y = 24 ------------ (2)

On solving (1) * 5 & (2), we get

10x - 5y = -10

11x - 5y = 24

--------------------

-x = -34

x = 34.

Substitute x = 34 in (1), we get

= > 2x - y = -2

= > 2(34) - y = -2

= > 68 - y = -2

= > -y = -70

= > y = 70.

Therefore, the two numbers are 34 and 70.

Hope this helps!