model 3 fraction of numbers Practice Questions Answers Test with Solutions & More Shortcuts

Question : 31 [SSC CGL 2008]

By how much does $6/\text"7/8"$ exceed $\text"6/7"/8$ ?

a) 7 $5/6$

b) 7 $3/4$

c) 6 $3/4$

d) 6 $1/8$

Answer: (c)

$6/{7/8} = {6×8}/7 = 48/7$

= ${6/7}/8 = 6/{7×8} = 3/28$

Required difference = $48/7 – 3/28$

= ${192 - 3}/28 = 189/28 = 27/4 = 6{3}/4$

Question : 32

A tin of oil was 4 5 full. When 6 bottles of oil was taken out and 4 bottles of oil was poured into it, it was $3/4$ full. How many bottles of oil can the tin contain ?

a) 40

b) 30

c) 20

d) 10

Answer: (a)

Let the tin contain x bottles of oil.

As given,

$4/5x – 6 + 4 = 3/4x$

$4/5x – 3/4 x$ = 2

$({16 – 15}/20)x$ = 2

$x/20$ = 2 ⇒ x = 2 × 20 = 40

The tin can contain 40 bottles.

Question : 33 [SSC CGL Prelim 2005]

The product of two fractions is $14/15$ and their quotient is $35/24$. The greater of the fractions is

a) $4/5$

b) $7/3$

c) $7/6$

d) $7/4$

Answer: (c)

Let the fractions be x and y, where x > y

$xy = 14/15$ and $x/y = 35/24$

$xy × x/ y$ = $14/15× 35/24$

$x^2$ = $49/36$⇒ $x = 7/6$

Question : 34 [SSC CGL Tier-I 2010]

The number 0.121212.... in the form $\text"p"/\text"q"$ is equal to

a) $2/33$

b) $4/33$

c) $2/11$

d) $4/11$

Answer: (b)

0.121212 .... = 0.$\ov{12}$ = $12/99 = 4/33$

Question : 35 [SSC FCI Assistant 2012]

The value of ${1/15 + 1/35 + 1/63 + 1/99 + 1/143}$ is

a) $7/39$

b) $2/39$

c) $4/39$

d) $5/39$

Answer: (d)

$1/15 + 1/35 + 1/63 + 1/99 + 1/143$

= $1/{3×5}+1/{5×7}+1/{7×9}+1/{9×11}+1/{11×13} $

=$1/2(1/3 - 1/5+1/5 - 1/7+1/7 - 1/9+1/9 - 1/11+1/11 - 1/13)$

=$1/2(1/3 - 1/13)$

= $1/2({13 - 3}/39) = 5/39$

IMPORTANT quantitative aptitude EXERCISES

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