Question

if 2 is added to numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it becomes 4/5 find the fraction
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Answer 1

Let the fraction be x / y. 

If 2 is added to the numerator and denominator fraction becomes 9/10 so,

(x + 2)/(y + 2) = 9/10

10 (x + 2) = 9 (y + 2) 

10x + 20 = 9y + 18

10x – 9y + 20 = 9y – 9y + 18

10x – 9x + 20 – 20 = 18 – 20 

10x – 9y = -2 ………. (i) 

If 3 is subtracted from numerator and denominator the fraction becomes 4/5 so,

(x – 3)/(y – 3) = 4/5

5(x – 3) = 4(y – 3) 

5x – 15 = 4y – 12

5x – 4y – 15 = 4y – 4y – 12 

5x – 4y – 15 + 15 = – 12 + 15

5x – 4y = 3 ………. (ii) 

 

Multiplying both sided of equation by 2, we get

10x – 8y = 6

Now, solving equation

10x – 9y = -2

10x – 8y =  6

        - y = - 8

y = 8 

Substituting the value of y ,

5x – 4 × (8) = 3

5x – 32 = 3

5x – 32 + 32 = 3 + 32

5x = 35

x = 35/5

x = 7

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Answer 2

Answer:

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