A fraction become $\frac{1}{6}$ when 4 is subtracted from its numerator and 1 is added to its denorninator. If 2 and 1 are respectively add… — Answer & Discussion

A fraction become $\frac{1}{6}$ when 4 is subtracted from its numerator and 1 is added to its denorninator. If 2 and 1 are respectively added to its numerator and the denominator , it becomes $\frac{1}{3}$ .Then , the LCM of the numerator and denominator of the said fraction , must be

A14
B350
C5
D70

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Discussion 2

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CCommunity20 Jan 2018

option 4 is the right answer

CCommunity10 Apr 2018

Let the original fraction be $\frac{X}{Y}$

$\frac{X-4}{Y+1}=\frac{1}{6}$

6x – 24 = y + 1
6x – y = 25 .......(i)

Again,

$\frac{X+2}{Y+1}=\frac{1}{3}$

3x + 6 = y + 1
Þ 3x – y = –5 .......(ii)
By equation (i) – (ii),
6x – y – 3x + y = 25 + 5
3x = 30

x = 10
From equation (i),
60 – y = 25 Þ y = 35
LCM of 10 and 35 = 70