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

Question : 21 [SSC CGL 2002]

A boy on being asked what $6/7$ of a certain fraction was, made the mistake of dividing the fraction by $6/7$ and so got an answer which exceeded the correct answer by $13/70$. Find the fraction–

a) $7/9$

b) $4/5$

c) $3/5$

d) $2/3$

Answer: (c)

Let the fraction = x

According to the question;

$6/7$ of x = $x/{6/7} - 13/70$

= $\text"6x"/7 = \text"7x"/6 - 13/70$

= $\text"7x"/6 - \text"6x"/7 = 13/70$

= $\text"49x - 36x"/42 = 13/70$

= $\text"13x"/42 = 13/70$

x = ${13×42}/{70×13} = 3/5$

Question : 22 [SSC CGL Prelim 2008]

A boy was asked to find $3/5$ of a fraction. Instead, he divided the fraction by $3/5$ and got an answer which exceeded the correct answer by $32/75$ . The correct answer is

a) $2/15$

b) $2/25$

c) $6/25$

d) $3/25$

Answer: (c)

Let the fraction be x,

According to the question,

$x/{3/5}$ - $x × 3/5 = 32/75$

${5x}/3$ - ${3x}/5 = 32/75$

${25x – 9x}/15 = 32/75$

${16x}/15 = 32/75$

$x = 32/75 × 15/16 = 2/5$

Correct answer = $2/5 × 3/5 = 6/25$

Question : 23

Two-third of a positive number and $25/216$ of its reciprocal are equal. The number is

a) $12/5$

b) $144/25$

c) $5/12$

d) $25/144$

Answer: (c)

Let the number be x.

$2/3$x = $25/\text"216x"$⇒ $x^2 = {25×3}/{2×216}$

x = $√{{25×3}/{2×216}}$ = $√{25/144}$ = $5/12$

Question : 24 [SSC CGL 2002]

$1/2$ of $3/4$ of a number is 2$1/2$ of 10. What is the number?

a) 56

b) 66$2/3$

c) 60

d) 50

Answer: (b)

Let the number is x.

According to the question

$1/2$ of $3/4$ of x = 2$1/2$ of 10

=$\text"3x"/8 = 5/2$ × 10

x = ${5×10×8}/{3×2} = 200/3 =66{2/3}$

Question : 25 [SSC FCI Assistant 2012]

A tree increases annually by $1/8$th of its height. By how much will it increase after 2 years, if it stands today 64 cm high?

a) 81 cm

b) 75 cm

c) 74 cm

d) 72 cm

Answer: (a)

Height of tree after 1 year = 64 + 64 × $1/8$= 72 cm

Height of tree after 2 years = 72 + 72 × $1/8$

= 72 + 9 = 81 cm

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