Question

the denominator of a rational number is 1 more than its numerator. if numerator is reduced by 2 and denominator is decreased by 3 the rational number reduces to 1/4......find the rational number​

Answer 1

Answer:

Let the numerator of the rational number be x.

Then, the denominator of the rational number =x+6.

It is given that the numerator is increased by 5 and the denominator is decreased by 3.

∴ the numerator of the new rational number =x+5.

Denominator of the new rational number =(x+6)−3=x+3

∴ new rational number =

x+3

x+5

But the new rational number is given as

4

5

.

∴

x+3

x+5

=

4

5

By cross multiplying, we get,

4(x+5)=5(x+3)

⇒4x+20=5x+15

⇒4x−5x=15−20 ....[Transposing 5x to LHS. and 20 to RHS]

⇒−x=−5 or x=5

∴ numerator of the rational number is 5 and denominator = 5+6 i.e. 11.

∴ the required rational number is

11

5

Step-by-step explanation:

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Answer 2

Correct Question:

the denominator of a rational number is 1 more than its numerator. if numerator is reduced by 2 and denominator is increased by 3 the rational number reduces to 1/4......find the rational number

SOLUTION:

Let the fraction be x/y.

So, ATQ, we have

x+1 = y....(1)

Also, we have

(x-2)/(y-3) = 1/4

From eq(1), we get

(x-2)/(x+1+3) = 1/4

4x-8 = x+4

3x = 12

x = 4

So, y = 5

So, the rational number is 4/5

Hope this helps