Question

Two numbers are in the ratio 3: 4. If 2 is subtracted from each number, the ratio becomes 2:3. Find the numbers.​

Answer 1

The numbers are 6 and 8.

Explanation:

Let the numbers be x and y.

x/y = 3/4

(x - 2)/(y - 2) = 2/3

3y = 4x

2(y - 2) = 3(x - 2)

3y = 4x

2y - 4 = 3x - 6

4x - 3y = 0

3x - 2y = 2

-8x + 6y = 0

+ 9x - 6y = 6

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x = 6

3y = 4x

3y = 4 × 6

3y = 24

y = 8

The numbers are 6 and 8.