Question

Two numbers in the ratio 2 ; 3, if 5 is added to each number then the ratio become 5 ; 7 . Find the number .

Answer 1

The two numbers are 20 and 30

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Answer 2

Let the numerator no. = x

Let the denominator no. = y

According to the question,

x/y=2/5

x =2y/5 -----------(i)

If 5 is added,

(x+5)/(y+5) =5/7

7(x+5)=5(y+5)

7x + 30=5y + 25

5y - 7x = 30 - 25

5y - 7x = 5 ------------(ii)

Putting the value of x from eqn (i)

5y - 7(2y/5)=5

5y - 14y/5=5

(25y - 14y)/5=5

11y = 25

y= 25/11

Putting this value in eqn (i)

2(25/11)/5

50/11 × 5

50/55

10/11

So the numbers are 25/11 and 10/11.