Question

The denominator of a fraction is 3 more than the numerator , if 2 is added to the numerator and 5 is added to the denominator, the fraction becomes 1/2. Find the fraction.

Answer 1

⠀⠀ || ✪ Solution ✪ ||

Given:-

• The denominator of a fraction is 3 more than the numerator
• if 2 is added to the numerator and 5 is added to the denominator, the fraction becomes 1/2.

Find:-

• what is fraction .

|| ✪ Explanation ✪ ||

Let,

• Numerator = x
• Denominator = y

A/c to question,

(The denominator of a fraction is 3 more than the numerator)

➠ y = 3 + x

➠ x - y = -3 ...................(1)

And,

( if 2 is added to the numerator and 5 is added to the denominator, the fraction becomes 1/2 )

➠ (x+2)/(y+5) = 1/2

➠ 2.(x+2) = (y+5)

➠ 2x - y = 5 - 4

➠ 2x - y = 1 ......................(2)

Subtract equ(1) - equ(2),

➠ (x-2x) = (-3-1)

➠ -x = -4

➠ x = 4

keep value of x in equ(1),

➠ 4 - y = -3

➠ y = 4 + 3

➠ y = 7

Thus:-

• Fraction will be = 4/7 [Ans]

|| ✪ Verification ✪ ||

(The denominator of a fraction is 3 more than the numerator)

➠ y = 3 + x.

➠ 7 = 3 + 4

➠ 7 = 7

L.H.S = R.H.S

( if 2 is added to the numerator and 5 is added to the denominator, the fraction becomes 1/2 )

➠ (x+2)/(y+5) = 1/2

➠ (4+2)/(7+5) = 1/2

➠ 6/12 = 1/2

➠ 1/2 = 1/2

L.H.S = R.H.S

That's proved

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