Question

3. The numerator of a fraction is 3 less than its denominator If the numerator is increased by 1
and the denominator is increased by 3, the fraction becomes Find the original fraction.​

Answer 1

$\mathcal{\huge{\underline{\underline{\green{Solution:-}}}}}$

The numerator of a fraction is 3 less than its denominator.

According to question,

=> N = M - 3 _______ (eq 1)

➡ If the numerator is increased by 1 and the denominator is increased by 3 the fraction becomes 1/2.

According to question,

$= > \dfrac{N + 1}{M + 3} = \dfrac{1}{2}$

Cross multiply them

=> 2(N + 1) = 1(M + 3)

=> 2N + 2 = M + 3

=> 2N - M = 3 - 2

=> 2N - M = 1

=> 2(M - 3) - M = 1 [From (eq 1)]

=> 2M - 6 - M = 1

=> M - 6 = 1

=> M = 1 + 6

=> M = 7 (denominator)

Put value of M in (eq 1)

=> N = 7 - 3

=> N = 4 (numerator)

______________________________

Answer ✒Fraction = $\dfrac{4}{7}$

☆ VERIFICATION ⭐

From above , M = 7 and N = 4

Put value of M and N in this :

➡$\dfrac{ N + 1}{ M + 3} = \dfrac{1}{2}$

➡$\dfrac{4 + 1}{7 + 3} = \dfrac{1}{2}$

➡$\dfrac{5}{10} = \dfrac{1}{2}$

➡$\dfrac{1}{2} = \dfrac{1}{2}$

➡LHS = RHS

Hence, Verified ✅

________________________________

Answer 2

$\large\bf{\underline{Correct\: Question:-}}$

The numerator of a fraction is 3 less than its denominator If the numerator is increased by 1

and the denominator is increased by 3, the fraction becomes 1/2 .Find the original fraction.

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

• The numerator of a fraction is less than its denominator.
• if numerator increased by 1 denominator decreased by 3 then fracfion be become 1/2

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

• Original fraction = ?

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

$→\tt Let\:denominator\:be\:x\\\tt→ And\: numerator\:be=x-3$

$\large\bf{\underline{According\:to\: Question:-}}$

$\leadsto\tt (\frac{x-2}{x-3})=\frac{1}{2}\\\tt\leadsto 2x-4=x+3\\\tt\leadsto 2x-x=3+4\\\tt\leadsto x=7$

$\large\tt\implies\: Denominator=7\\\tt\large\implies\: numerator= x-3=7\\\tt\large\implies x=4\\\tt\large\implies\: fraction=\frac{4}{7}$