# Fraction Questions for Competitive Exams

Fractions are an integral component of the Number System. Fraction questions are commonly found in competitive exams. To aid in preparation, an online test in both Hindi and English has been made available to sharpen one’s Maths skills.

## Number System Type 3 : Fraction of numbers

Question 1:
A runner runs 1$\frac{1}{4}$ laps of a 5 lap race. What fractional part of the race remains to be run?
एक धावक 5 लैप की दौड़ में 1$\frac{1}{4}$ लैप दौड़ता है। दौड़ का कौन-सा भिन्नात्मक भाग चलाना बाकी है?

(1) $\frac{15}{4}$
(2) $\frac{4}{5}$
(3) $\frac{5}{6}$
(4) $\frac{2}{3}$

(1) $\frac{15}{4}$
Remaining race
= 5-1$\frac{1}{4}$ laps
= 5- $\frac{5}{4}$ laps
=$\frac{15}{4}$ laps

Question 2:
$\frac{1}{2} of \frac{3}{4} of a number is 2 \frac{1}{2}$ of 10.What is the number?
किसी संख्या का \frac{3}{4} का $\frac{1}{2}$ 10 का 2 $\frac{1}{2}$ है। संख्या क्या है?

(1) 50
(2) 60
(3) 66 $\frac{2}{3}$
(4) 56

(3) 66 $\frac{2}{3}$
Let the number is x.
According to the question
$\frac{1}{2}$ of $\frac{3}{4}$ of x = 2 $\frac{1}{2} of 10$
$\frac{3x}{8}= \frac{5}{2}$
x=$\frac{ 5.10.8}{ 3. 2}$ = $\frac{200}{3}$ = $66\frac{2}{3}$

Question 3:
Difference between the reciprocal of a positive proper fraction and the fraction itself be $frac{9}{20}$ , then the fraction is
यदि किसी धनात्मक उचित भिन्न के व्युत्क्रम और स्वयं भिन्न के बीच का अंतर $frac{9}{20}$ है, तो भिन्न है

(1) $\frac{3}{5}$
(2) $\frac{3}{10}$
(3) $\frac{4}{5}$
(4) $\frac{5}{4}$

(3) $\frac{4}{5}$
The required fraction is $\frac{4}{5}$, because
=$\frac{5}{4}$$\frac{4}{5}$
=$\frac{25-16}{20}$
=$\frac{9}{20}$

Question 4:
In a class, there are ‘z’ students. Out of them ‘x’ are boys. What part of the class is composed of girls ?
एक कक्षा में ‘z’ विद्यार्थी हैं। उनमें से ‘x’ लड़के हैं। कक्षा का कौन सा भाग लड़कियों से बना है?

(1) $\frac {x}{z}$
(2) $\frac {z}{x}$
(3) $1- \frac {x}{z}$
(4) $\frac {x}{z}$ -1

Boys = x
Girls = z – x
Part of girls = $\frac{z-x}{z}$
= 1- $\frac{x}{z}$

Question 5:
0.393939 ……. is equal to
0.393939 ……. के बराबर है
(1) $\frac{39}{100}$
(2) $\frac {13}{33}$
(3) $\frac {93}{100}$
(4) $\frac {39}{990}$

(2) $\frac {13}{33}$
= $\frac{39}{99}$
= $\frac{13}{33}$