Question

If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions.​

Answer 1

⠀⠀ıllıllı uoᴉʇnloS ıllıllı

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Let the fraction be x/y.

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

(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, We have:

(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)

So, We have:

• 10x – 9y = – 2 ………. (iii)
• And 5x – 4y = 3 ………. (iv)

Multiplying both sided of equation (iv) by 2, We get:

10x – 8y = 6 ………. (v)

Now, solving equation (iii) and (v),

We get:

10x – 9y = -2

10x – 8y = 6

⠀⠀⠀⠀- y = - 8

⠀⠀⠀⠀⠀y = 8

Substituting the value of y in equation (iv),

We get:

5x – 4 × (8) = 3

➠ 5x – 32 = 3

➠ 5x – 32 + 32 = 3 + 32

➠ 5x = 35

➠ x = 35/5

➠ x = 7

• Therefore, fraction becomes 7/8.

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