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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.
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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