model 3 fraction of numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions

MOST IMPORTANT quantitative aptitude - 6 EXERCISES

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The following question based on number system topic of quantitative aptitude

Questions : 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

The correct answers to the above question in:

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

Practice number system (model 3 fraction of numbers) Online Quiz

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Read more fractional numbers Based Quantitative Aptitude Questions and Answers

Question : 1

$2/3$ of three-fourth of a number is :

a) $17/12$ of the number

b) $8/9$ of the number

c) $1/3$ of the number

d) $1/2$ of the number

Answer: (d)

$2/3 × 3/4 = 1/2$

Question : 2

$1.\ov{27}$ in the form $\text"p"/\text"q"$ is equal to

a) $11/14$

b) $14/11$

c) $73/100$

d) $127/100$

Answer: (b)

1.$\ov{27}$ =1$27/99 = 1{3}/11 = 14/11$

Question : 3

Which of the following fraction is greater than $3/4$ but less than $5/6$ ?

a) $9/10$

b) $4/5$

c) $1/2$

d) $2/3$

Answer: (b)

Decimal equivalent of :

$3/4$ = 0.75 and $5/6$ = 0.833

Now, $2/3$ = 0.66, $1/2$ = 0.5 ,

$4/5$ = 0.8 and $9/10$ = 0.9

Clearly, $4/5$ lies between $3/4$ and $5/6$.

Question : 4

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 : 5

$0.4\ov{23}$ 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 : 6

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)

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

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