Question

plz explain this question​

Answer 1

Solution

Given:-

• if 2 added to both the numerator and denominator then its became 9/11
• If 3 added to both the numerator and denominator then its became 5/6

Find:-

• Fraction = ?

Explanation

Let,

• Numerator = x.
• Denominator = y

A/c to question

( if 2 added to both the numerator and denominator then its became 9/11 )

➥ (x+2)/(y+2) = 9/11

➥ 11.(x+2) = 9.(y+2)

➥ 11x - 9y = 18 - 22

➥ 11x - 9y = -4 ..........(1)

And,

( If 3 added to both the numerator and denominator then its became 5/6 )

➥(x+3)/(y+3) = 5/6

➥6.(x+3) = 5.(y+3)

➥6x - 5y = - 18 + 15

➥ 6x - 5y = -3 .................(2)

Multiply by 6 in equ(1) and 11 in equ(2)

• 66x - 54y = -24
• 66x - 55y = -33

_____________Sub. it's (eliminate x )

➥ y = 9

Keep value of y in equ(1)

➥ 11x - 9 × 9 = -4

➥ 11x = -4 + 81

➥ 11x = 77

➥ x = 77/11

➥x = 7

Thus:-

• value of x = 7
• Value of y = 9

Hence:-

• fraction will be = x/y = 7/9. [Ans.]

Verification

( if 2 added to both the numerator and denominator then its became 9/11 )

➥(x+2)/(y+2) = 9/11

➥ (7+2)/(9+2) = 9/11

➥ 9/11 = 9/11

L.H.S = R.H.S

And,

( If 3 added to both the numerator and denominator then its became 5/6 )

➥ (x+3)/(y+3) = 5/6

➥ (7+3)/(9+3) = 5/6.

➥ 10/12 = 5/6

➥ 5/6 = 5/6

L.H.S = R.H.S

That's proved.