Model 3 Fraction Of Numbers Practice Questions Answers Test With Solutions & More Shortcuts

Question : 11 [SSC CPO S.I.2006]

If the difference between the reciprocal of a positive proper fraction and the fraction itself be $9/20$ , then the fraction is

a) $5/4$

b) $4/5$

c) $3/10$

d) $3/5$

Answer: (b)

The required fraction is $4/5$, because $5/4$ – $4/5$

=${25 - 16}/20 = 9/20$

Question : 12 [SSC SO 2003]

When $0.\ov{47}$ is converted as a fraction, the result is

a) $47/99$

b) $46/99$

c) $46/90$

d) $47/90$

Answer: (a)

$0.\ov{47} = 47/99$

Question : 13 [SSC CPO S.I. 2005]

$0.4\ov{23}$ is equivalent to the fraction :

a) $94/99$

b) $49/99$

c) $419/990$

d) $491/990$

Answer: (c)

$0.4\ov{23} = {423- 4}/990 = 419/990$

Question : 14 [SSC CHSL 2011]

The denominator of a fraction is 3 more than its numerator. If the numerator is increased by 7 and the denominator is decreased by 2, we obtain 2. The sum of numerator and denominator of the fraction is

a) 19

b) 17

c) 13

d) 5

Answer: (c)

Let the original fraction be $x/{x + 3}$.

${x + 7}/{x + 3 - 2} = 2$

$x + 7 = 2x + 2$

$x = 7 - 2 = 5$

Required sum =$x + x + 3 = 2x + 3 = 10 + 3 = 13$

Question : 15

The sum of the numerator and denominator of a positive fraction is 11. If 2 is added to both numerator and denominator, the fraction is increased by $1/24$. The difference of numerator and denominator of the fraction is

a) 9

b) 1

c) 3

d) 5

Answer: (b)

Let numerator be $x$, then denominator = 11 – $x$.

Fraction =$x/{11 - x}$

Again, ${x + 2}/{11 – x + 2} = x/{11 - x} + 1/24$

⇒ ${x + 2}/{13 - x} – x/{11 - x} = 1/24$

⇒ ${11x – x^2 + 22 – 2x – 13x +x^2}/{(13 - x)(11 - x)} = 1/24$

⇒ ${22 – 4x}/{(13 - x)(11 - x)} = 1/24$

⇒ $528 – 96x = 143 – 24x + x^2$

⇒ $x^2 + 72x – 385$ = 0

⇒ $x^2 + 77x – 5x – 385$ = 0

⇒ $x (x + 77) - 5 (x + 77)$ = 0

⇒ (x - 5) (x + 77) = 0 ⇒ x = 5

Denominator = 11 - 5 = 6

Difference = 6 - 5 = 1

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