Question

The denominator of a rational number is 4 more than the numerator. if the numerator and the denominator are increased by 1 each, the rational number becomes 1/2. find the number.​

Answer 1

Answer:

Let the numerator of the rational number be x.

Then, the denominator of the rational number =x+4

It is given that the numerator is increased by 2 and the denominator is increased by 3 to get the new rational number

4

3

.

According to the given condition,

(x+4)+3

x+2

=

4

3

By cross multiplying, we get

4(x+2)=3(x+7)

⟹4x+8=3x+21

⟹4x−3x=21−8 ....[Transposing 3x to LHS and 8 to RHS]

or x=13

Therefore, numerator of the rational number =13 and denominator =13+4=17.

Hence the original rational number is

17

13

.

Answer 2

Correct option is

C

17

13

Let the numerator of the rational number be x.

Then, the denominator of the rational number =x+4

It is given that the numerator is increased by 2 and the denominator is increased by 3 to get the new rational number

4

3

.

According to the given condition,

(x+4)+3

x+2

=

4

3

By cross multiplying, we get

4(x+2)=3(x+7)

⟹4x+8=3x+21

⟹4x−3x=21−8 ....[Transposing 3x to LHS and 8 to RHS]

or x=13

Therefore, numerator of the rational number =13 and denominator =13+4=17.

Hence the original rational number is

17

13

.