Question

8. Two numbers are such that the ratio between them is 3:5. If each is increased by 10, the
ratio between the new numbers so formed is 5 : 7. Find the original numbers.
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Answer 1

Answer:

Step-by-step explanation:

Given The ratio of the 2 no. is = 3:5

Let the no. be 3x and 5x

If each one is increased by 10

They wil become = 3x + 10 and  5x + 10

A/Q,

       3x + 10 / 5x + 10 = 5 / 7

       7 ( 3x + 10) = 5 ( 5x + 10)

        21x + 70 = 25x + 50

        21x - 25x  = 50 - 70

      - 4x = -20

         x = 20 / 4

       So, x = 5

Now,

The no. are =3x

= 3 × 5

= 15

And  

5x

= 5 × 5

= 25

Answer 2

ratios of numbers = 3 : 5

let the constant ratios be x

ratios now become = 3x : 5x

after adding 10 to both the rational sides ==>

3x + 10 : 5x + 10  =  5x : 7x

let the ratios be put in fractional form.

3x + 10 = 5x

5x + 10 = 7x

cross multiplication

7x ( 3x + 10 ) = 5x ( 5x + 10 )

=> 21x^2 + 70x = 25x^2 + 50x

=> 21x^2 - 25x^2 = 50x - 70x

=> -4x^2 = -20x

=> 4x^2 = 20x

=> x^2 = 20x/4

=> x^2 = 5x

=> x * x = 5 * x

=> x = 5

number 1 = 3x = 3 * 5 = 15

number 2 = 5x = 5 * 5 = 25

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