Fraction questions

The fractional questions suggested here will assist learners in understanding how to approach arithmetic questions using fractions. We are given expert solutions with simple tricks and shortcuts to solve fraction-based problems based asked in several competitive tests such as Kerala PSC, Banking, RBI Assistant, LIC, SSC, MBA - MAT, CAT, UPSC, NET, etc. So why wait? Find the questions for free now!

  1. When the numerator of a fraction is increased by \(10 \%\) and its denominator is increased by \(20 \%\) then, the fraction becomes \(\frac{1}{2}\). If denominator is 5 morc than the numerator, what will be the original fraction ?

Answer: Option C

(C) \(\frac{6}{11}\)

Let original fraction \(=\frac{x}{y}\)

Therefore, \(\frac{x \times \frac{110}{100}}{y \times \frac{120}{100}}=\frac{1}{2} \quad\)

\( \frac{x\times110}{y\times 120}= \frac{1}{2} \)

\(\frac{x}{y} = \frac{1\times120}{2\times 110} \)


  1. A fraction becomes \(\frac{1}{3}\) when 1 is substracted from the numerator and it becomes \(\frac{1}{4}\) when 8 is added to its denominator. The fraction is

Answer: Option C

Let the fraction be \(\frac{x}{y}\).

As per the question, \(\frac{x - 1}{y} = \frac{1}{3} \Rightarrow 3(x- 1) = y \Rightarrow 3x - y = 3\) ...(1)

and \(\frac{x}{y+8} = \frac{1}{4} \Rightarrow 4x = y+8\Rightarrow 4x - y = 8\) ...(2)

Substracting equation (2) from (1), we get \(x = 5\) and substituting it in equation (1), then, \((3 \times 5) - y = 3\)

\(\Rightarrow 15 - y = 3 \Rightarrow y = 12\)

Therefore, fraction is \(\frac{x}{y}\) = \(\frac{5}{12}\)

  1. If 1 is added to the denominator of a fraction, the fraction becomes \(\frac{1}{2}\). If 1 is added to the numerator of the fraction, the fraction becomes 1 . The sum of the numerator and denominator of the fraction is

Answer: Option B

Let the fraction be \(\frac{x}{y}\)

According to question,


\(2 x=y+1\)

\(2 x-y=1 \ldots(\mathrm{i})\)

\(\& \frac{x+1}{y}=1\)


\(x-y=-1 \ldots \ldots(i i)\)

now, equation \((i)-\) equation \((i i)\)

we get, \(x=2\)

and \(y=3\)

Therefore, fraction \(\frac{x}{y}=\frac{2}{3}\)

Hence, the sum of the numerator and denominator of the fraction \(=2+3=5\)

  1. The difference between \(\frac{3}{5}\) of \(\frac{1}{2}\) of a number and \(\frac{1}{4}\) of \(\frac{2}{5}\) of the same number is \(140 .\) Determine the number?

Answer: Option D

Let the number be \(x\)

According to the question

\(\frac{3}{5} \times \frac{1}{2} \times x-\frac{1}{4} \times \frac{2}{5} \times x=140\)

\(\frac{3 x}{10}-\frac{x}{10}=140\)

\(\frac{2 x}{10}=140\)

\(\therefore x=700\)

Hence, option D is correct.

  1. If 0.44 is written as in fraction, what will be the sum of its numerator and denominator?

Answer: Option C

0.44 can be written as \(\frac{44}{100} = \frac{11}{25}\) in fraction.

so, numerator = 11 and denominator = 25

sum of its numerator and denominator = 11 + 25 = 36