If we add 1 to the numerator of a fraction becomes 1/2 and if 5 is subtracted from the denominator, it becomes 1. Find the fraction

Question

If we add 1 to the numerator of a fraction becomes 1/2 and if 5 is subtracted from the denominator, it becomes 1. Find the fraction

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2 months 2021-11-23T05:21:57+00:00 2 Answers 0 views 0

1. Solution

Given :

• If we add 1 to the numerator of a fraction becomes 1/2
• if 5 is subtracted from the denominator, it becomes 1.

Find :

• These fraction

Explanation

Let,

• Numerator be = x
• Denominator be = y

A/C to question,

(If we add 1 to the numerator of a fraction becomes 1/2)

==> (x+1)/y = 1/2

==> 2x – y = -2 (1)

Again,

(if 5 is subtracted from the denominator, it becomes 1.)

==> x/(y-5) = 1

==> x – y = -5 (2)

Subtract equ(1) & equ(2)

==> 2x – x = -2 + 5

==> x = 3

Keep Value of x in equ(1)

==> 2 × 3 – y = -2

==> y = 6 + 2

==> y = 8

Hence

• Fraction will be (x/y) = 3/8

_________________

Case(1).

(If we add 1 to the numerator of a fraction becomes 1/2)

==> (3+1)/8 = 1/2

==> 4/8 = 1/2

==> 1/2 = 1/2

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

Case(2).

(if 5 is subtracted from the denominator, it becomes 1.)

==> 3/(8-5) = 1

==> 3/3 = 1

==> 1 = 1

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

Thats proved.

_______________

2. Given :-

If we add 1 to the numerator of a fraction becomes 1/2

if 5 is subtracted from the denominator, it becomes 1.

TO Find :-

These fraction

Explanation

Let,

Numerator be = x

Denominator be = y

A/C to question,

(If we add 1 to the numerator of a fraction becomes 1/2)

==> (x+1)/y = 1/2

==> 2x – y = -2 ——–(1)

Again,

(if 5 is subtracted from the denominator, it becomes 1.)

==> x/(y-5) = 1

==> x – y = -5 ———-(2)

Subtract equ(1) & equ(2)

==> 2x – x = -2 + 5

==> x = 3

Keep Value of x in equation (1)

==> 2 × 3 – y = -2

==> y = 6 + 2

==> y = 8

Hence

Fraction will be (x/y) = 3/8

_________________

Case(1).

(If we add 1 to the numerator of a fraction becomes 1/2)

==> (3+1)/8 = 1/2

==> 4/8 = 1/2

==> 1/2 = 1/2

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

Case(2).

(if 5 is subtracted from the denominator, it becomes 1.)

==> 3/(8-5) = 1

==> 3/3 = 1

==> 1 = 1

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