Question

if we add 1 to numerator of a fraction , it reduced to 1/2 if we subtract 1 from the denominator it reduces to 1/3 find the fraction by substitution method
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Answer 1

Answer:

let fraction be a/b

a+1=1/2

a=1/2-1

a=-1/2

b-1=1/3

b=1/3+1

b=4/3

-1/2 × 3/4

-3/8 is the answer

Answer 2

$\large\bf\underline{Given:-}$

• if we add 1 to numerator of a fraction , it reduced to 1/2 if we subtract 1 from the denominator it reduces to 1/3 .

$\large\bf\underline {To \: find:-}$

• Fraction.

$\huge\bf\underline{Solution:-}$

Let the numerator and denominator be x and y

• then fraction = x/y

$\underbrace{ \bf \: According \: to \: 1st \: condition}$

if we add 1 to numerator of a fraction , it reduced to 1/2.

$\longrightarrow \rm \: \frac{x + 1}{y} = \frac{1}{2} \\ \\ \longrightarrow \rm \: 2(x + 1) = y \\ \\ \longrightarrow \rm \: 2x + 2 = y \\ \\ \longrightarrow \rm \: y = 2x + 2.......(i)$

$\underbrace{ \bf \: According \: to \: 2nd \: condition}$

if we subtract 1 from the denominator it reduces to 1/3.

$\longrightarrow \rm \: \frac{x}{y - 1} = \frac{1}{3} \\ \\ \longrightarrow \rm \:3x = y - 1 \\ \\ \longrightarrow \rm \: x = \frac{y - 1}{3} ......(ii) \\ \\ \rm \: substituting \: value \: of \: y \: in \: eq \: .(ii)$

$\longrightarrow \rm \: \frac{x}{y - 1} = \frac{1}{3} \\ \\ \longrightarrow \rm \:3x = y - 1 ......(ii) \\ \\ \rm \: substituting \: value \: of \: y \: in \: 2nd \\ \longrightarrow \rm3x = 2x + 2 - 1 \\ \\ \longrightarrow \rm \: 3x - 2x = 1 \\ \\ \longrightarrow \rm \: x = 1$

Substituting value of x in eq.(i)

$\longrightarrow \rm \: y = 2x + 2 \\ \\ \longrightarrow \rm \: y = \:2 \times 1 + 2 \\ \\ \longrightarrow \rm \:y = 2 + 2 \\ \\ \longrightarrow \rm \:y = 4$

• So, x = 1 and y = 4.

So, the fraction = 1/4