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If 1 is subtracted from both its numerator and denominator then fraction becomes 1/3 . If numerator and denominator are added by 1, it becomes 1/2. Find the fraction.
CBSE | Class 10 | Exercise 3.8 | Maths | Pair of Linear Equations In Two Variables | RD Sharma
If 1 is subtracted from both its numerator and denominator then fraction becomes 1/3 . If numerator and denominator are added by 1, it becomes 1/2. Find the fraction.

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

So, the required fraction is A/B.

ATQ,

Thus, the equation so formed is,

(A-1)/(B−1)=1/3

⇒ 3(A-1)=(B-1)

⇒ 3A-3=B-1

⇒ 3A-B-2=0…. (i)

And also it’s given in the question as,

If numerator and denominator are added by 1, it becomes 1/2 , so now the expression is

(A+1)/(B+1)=1/2

⇒ 2(A+1)=(B+1)

⇒ 2A+2=B+1

⇒ 2A-B+1=0 …….. (ii)

Solving (i) and (ii), to find the fraction

By using cross-multiplication, we will get

\begin{array}{l} \frac{A}{{( - 1) \times 1 - ( - 1) \times ( - 2)}} = \frac{{ - B}}{{3 \times 1 - 2 \times ( - 2)}} = \frac{1}{{3 \times ( - 1) - 2 \times ( - 1)}}\\ \frac{A}{{ - 1 - 2}} = \frac{{ - B}}{{3 + 4}} = \frac{1}{{ - 3 + 2}}\\ \frac{A}{{ - 3}} = \frac{{ - B}}{7} = \frac{1}{{ - 1}}\\ \frac{A}{3} = \frac{B}{7} = 1 \end{array}

⇒ A=3, B=7

Hence, the fraction is 3/7.

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