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Home » The denominator of a fraction is more than the numerator. If the denominator is eight times the numerator then the numerator is lessen by and denominator is increased by . Find the original fraction calculated.
The denominator of a fraction is 4 more than the numerator. If the denominator is eight times the numerator then the numerator is lessen by 2 and denominator is increased by 1. Find the original fraction calculated.
CBSE | Class 10 | Exercise 3.8 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
The denominator of a fraction is 4 more than the numerator. If the denominator is eight times the numerator then the numerator is lessen by 2 and denominator is increased by 1. Find the original fraction calculated.

Let the numerator of the fraction to be A and the denominator of the fraction to be B.

So, fraction is A/B.

The numerator of the fraction is 4 less the denominator.

Thus, the equation so formed is,

A=B-4

⇒ A-B=−4 …… (i)

ATQ,

B+1=8(A-2)

⇒ B+1=8A-16

⇒ 8A-B=1+16

⇒ 8A-B=17 …… (ii)

Solving (i) and (ii),

Subtract the equation (ii) from (i), we get

(A-B)-(8A-B)=-4-17

⇒ A-B−8A+B=−21

⇒ −7A=−21

⇒ A=21/7

⇒ A=3

Substituting the value of A=3 in the equation (i), we find B

3-B=- 4

⇒ B=3+4

⇒ B=7

Therefore, the fraction is 3/7.

i

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