Question

the denominator of fraction is 6 more than the numerator. If 1 is added to the numerator and three subtracted from the denominator it becomes 3/4. find the fraction​

Answer 1

Question

the denominator of fraction is 6 more than the numerator. If 1 is added to the numerator and three subtracted from the denominator it becomes 3/4. find the fraction .

Solution

Given:-

• the denominator of fraction is 6 more than the numerator
• If 1 is added to the numerator and three subtracted from the denominator it becomes 3/4

Find:-

• fraction ?

Explanation

Let, Numerator is x and denominator is y

So, A/c to question

( the denominator of fraction is 6 more than the numerator )

➠ y = 6 + x

➠ x - y = -6 ............(1)

Again,

( If 1 is added to the numerator and three subtracted from the denominator it becomes 3/4 )

➠(x+1)/(y-3) = 3/4

➠ 4.(x+1) = 3.(y-3)

➠ 4x - 3y = -9 -4

➠ 4x - 3y = -13 .............(2)

Multiply by 4 in equ (1),

• 4x - 4y = -24
• 4x - 3y = -13

____________Sub. it's

➠ (-4y + 3y ) = (-24 + 13)

➠ -y = - 11

➠ y = 11

Keep value of y in equ(1),

➠ x - 11 = -6

➠ x = - 6 + 11

➠x = 5

Hence:-

• Value of numerator x = 5
• Value of denominators y = 11

Thus:-

• Fraction will be = x/y = 5/11

Verification

Case(1):-

( the denominator of fraction is 6 more than the numerator )

➠ y = 6 + x

➠ 11 = 5 + 6

➠ 11 = 11

L.H.S = R.H.S

Case(2):-

( If 1 is added to the numerator and three subtracted from the denominator it becomes 3/4 )

➠(x+1)/(y-3) = 3/4

➠(5+1)/(11-3) = 3/4

➠ 6/8 = 3/4

➠ 3/4 = 3/4

L.H.S. = R.H.S.

That's proved.