Practice Fractional numbers - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) A number exceeds its one-fifth by 20. The number is
(a)
(b)
(c)
(d)
Let the number be x.
According to the question,
x = $\text"x"/5$ + 20⇒ x - $\text"x"/5$ = 20
$\text"4x"/5$ = 20
x = ${20×5}/4 = 25$
Q-2) 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)
(b)
(c)
(d)
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
Q-3) If 3 times a number exceeds its $3/5$ by 60, then what is the number ?
(a)
(b)
(c)
(d)
Suppose required number is x Then,
3x -$\text"3x"/5$ = 60 ⇒ $\text"12x"/5$ =60
= x = ${60 × 5}/12$ = 25
Q-4) If 1 is added to the denominator of a fraction it becomes $1/2$. If 1 is added to the numerator it becomes 1. The product of numerator and denominator of the fraction is
(a)
(b)
(c)
(d)
Let the numerator = x and denominator = y
Fraction = $\text"x"/ \text"y"$ and $\text"x"/ \text"y+1" = 1/2$
2x = y + 1 ⇒ x =$\text"y+1"/2$
$\text"x+1"/\text"y"$ =1⇒ x+1 = y
$\text"y+1"/2$+1 = y
$\text"y+1+2"/2$ = y
y +3= 2y ⇒ y = 3
x +1= 3 ⇒ x = 2
∴ xy = 2 × 3 = 6
Q-5) An 85m long rod is divided into two parts. If one part is $2/3$of the other part, then the longer part (in metres) is :
(a)
(b)
(c)
(d)
Let the longer part be x
According to question,
Shortest part = $\text"2x"/3$
x + $2/3$x = 85m
= $\text"3x + 2x"/3$ = 85
= $\text"5x"/3$ = 85
∴ x = 51m
Q-6) If one-third of one-fourth of a number is 15, then three-tenth of the number is
(a)
(b)
(c)
(d)
Let the number be x.
= $x/{3 × 4}$ = 15
x = 15 × 3 × 4 = 180
Now, required number
= ${3/10}x = 3/10$ × 180 = 54
Q-7) 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)
(b)
(c)
(d)
Let the original fraction be $x/{x + 3}$.
${x + 7}/{x + 3 - 2} = 2$
$x + 7 = 2x + 2$
$x = 7 - 2 = 5$
Required sum =$x + x + 3 = 2x + 3 = 10 + 3 = 13$
Q-8) $1/2$ of $3/4$ of a number is 2$1/2$ of 10. What is the number?
(a)
(b)
(c)
(d)
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 = ${5×10×8}/{3×2} = 200/3 =66{2/3}$
Q-9) 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)
(b)
(c)
(d)
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.
Q-10) If one-nineth of a certain number exceeds its one-tenth by 4, the number is
(a)
(b)
(c)
(d)
Let the number be x.
According to the question
$x/9 - x/10$ = 4
${10x – 9x}/90$ = 4
x = 90 × 4 = 360