Question

Two numbers are in the ratio 7:5. If 2 is subtracted from each of them, the ratio becomes 3:2. Find the numbers.

Answer 1

Answer:

Step-by-step explanation:

Ratio = 7 : 5

Numbers are 7x , 5x

$\dfrac{7x-2}{5x-2}=\dfrac{3}{2}$

Cross multiply,

2*(7x - 2) = 3*(5x -2)

2*7x - 2*2 = 3*5x - 3*2

14x - 4       = 15x - 6    

14x - 4 + 6 = 15x   {Add 6 to both sides}

14x  + 2      = 15x

            2    = 15x - 14x       {Subtract '4x' from both sides}

   x = 2

7x = 7*2 = 14

5x = 5*2 = 10

Numbers are 14 , 10  

Answer 2

Answer:

The numbers are in the ratio 5:7

Let their common multiple be 'x'

The numbers are 5x, 7x

If 3 is subtracted from each of them the ratio becomes 2:3

5x-3/7x-3 = 2/3

3(5x-3) = 2(7x-3) (cross multiplication)

15x -9 = 14x -6

15x-14x = -6+9

x=+3

Therefore the numbers are 5* 3 =15, 7*3 = 21

(Verifications when 3 is subtracted from each other ,the ratio is 2/3, 15–3/21–3 = 12/18 = 2/3 ) verified)

The numbers are 15 & 21.

Step-by-step explanation:

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