Question

19) Two numbers are in the ratio 2 : 3. If 2 is subtracted from the first and 2 is added to the second, the ratio becomes 1:2.
The sum of the number is?


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Answer 1

Explanation:

Let the two numbers be 2x and 3x.

Given,

$\frac{2x - 2}{3x + 2} = \frac{1}{2}$

Cross multiply,

$2(2x - 2) = 3x + 2$

$4x - 4 = 3x + 2$

$4x - 3x = 2 + 4$

$x = 6$

Hence, the numbers are

$2x = 2 \times 6 = 12$

$3x = 3 \times 6 = 18$

Answer: 12 and 18

I hope this answer helps. :D

Answer 2

let the ratio be 2x : 3x

2x - 2 = 1

3x + 2 2

4x - 4 = 3x + 2

x = 6

2x = 12

3x = 18

sum of nos. = 30

hope it helps

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