Question

7. The denominator of a rational number is greater than its numerator by 3. If 3 is
subtracted from the numerator and 2 is added to its denominator the new number
becomes 1 by 5
Find the original number.​

Answer 1

Answer:

Let the numerator = x

So, x/x+3 is the original rational number.

Adding 2 to denominator and subtracting 3 from numerator

x - 3/ x + 9= 1/5

Cross multiplying

5x - 15 = x + 9

4x = 24

x = 24/4

x = 6

Original rational number is

6/13

6/13 is the original rational number

Answer 2

Solution

Given :-

• The denominator of a rational number is greater than its numerator by 3.
• If 3 is subtracted from the numerator and 2 is added to its denominator the new number becomes 1 by 5

Find :-

• These rational number .

Explanation

Let,

• Numerator be = x
• Denominator be = y

A/C to question,

(The denominator of a rational number is greater than its numerator by 3. )

==> y = x + 3

==> x - y = -3 ---------------Equ(1)

Again,

(If 3 is subtracted from the numerator and 2 is added to its denominator the new number becomes 1/5 )

==> (x-3)/(y+2) = 1/5

==> 5 * (x-3) = (y+2)

==> 5x - 15 = y + 2

==> 5x - y = 2 + 15

==> 5x - y = 17 --------------Equ(2)

Subtract equ(1) & equ(2)

==> x - 5x = -3 - 17

==> -4x = -20

==> x = -20/(-4)

==> x = 5

Keep Value of x in equ(1)

==> 5 - y = -3

==> y = 5 + 3

==> y = 8

Hence

• Fraction will be = x/y = 5/8

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