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?

Answer 1

Answer:

let the denominator be X.

then numerator will be X-3

Therefore, fraction will be X-3/X

From the given condition,

(X-3+1)/(X +3)=1/2

(X-2)/(X+3)=1/2

2(X-2)=1(X+3) (cross multiplied)

2x -4=x+3

2x -x =3+4

x=7

numerator =x-3=7-3=4

denominator =x=7

fraction =4/7

Answer 2

• Let denomination be M and numerator be N.

Fraction = $\dfrac{Numerator}{Denomination}\:=\:\dfrac{N}{M}$

》 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)

______________________________

Fraction = $\dfrac{4}{7}$

____________ [ ANSWER ]

_______________________________

☆ VERIFICATION :

From above calculations we have M = 7 and N = 4

Put value of M and N in this : $\dfrac{N\:+\:1}{M\:+\:3}\:=\:\dfrac{1}{2}$

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

=> $\dfrac{5}{10}\:=\:\dfrac{1}{2}$

=> $\dfrac{1}{2}\:=\:\dfrac{1}{2}$

_______________________________