problems-involving-fractions MCQs for UPSC Prelims

35 practice questions on problems-involving-fractions from the Working with Fractions section of the UPSC Prelims syllabus. 35 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

11 Easy 17 Medium 7 Hard

Sample questions

Q1
easy

A student says that $\frac{1}{2}$ of $30$ is $60$. Why must this be wrong?

  1. A $30$ is an even number
  2. B Half of a number is always smaller than the number
  3. C Half of a number is always a whole number
  4. D Halving and doubling give the same answer
Show answer and explanation

Correct answer: B - Half of a number is always smaller than the number

Taking half keeps only part of the quantity, so the answer has to be less than $30$, and $60$ is more. Whether the answer is a whole number is beside the point, as is the fact that $30$ is even. Halving and doubling move in opposite directions, which is exactly the mistake made here.

Q2
easy

If one fifth of a number is $7$, what is the number?

  1. A $1.4$
  2. B $12$
  3. C $\frac{7}{5}$
  4. D $35$
Show answer and explanation

Correct answer: D - $35$

The whole is made of five such parts, so the number is $7 \times 5 = 35$. The value $12$ comes from adding $5$ to $7$, $\frac{7}{5}$ from dividing by $5$, and $1.4$ is that same division written as a decimal.

Q3
hard

A shop starts the week with $120$ shirts. It sells $\frac{3}{4}$ of them on Monday and $\frac{1}{3}$ of the remaining shirts on Tuesday. How many shirts are left?

  1. A $10$
  2. B $20$
  3. C $30$
  4. D $40$
Show answer and explanation

Correct answer: B - $20$

Monday's sale is $120 \times \frac{3}{4} = 90$, leaving $30$ shirts. Tuesday's sale is $30 \times \frac{1}{3} = 10$, so $30 - 10 = 20$ shirts remain. The value $30$ stops after Monday, $10$ counts Tuesday's sale, and $40$ takes a third of the original stock instead of the remainder.

Q4
medium

A recipe for one cake needs $1\frac{1}{2}$ cups of flour. How much flour is needed for $3$ such cakes?

  1. A $3\frac{1}{2}$ cups
  2. B $4\frac{1}{6}$ cups
  3. C $4\frac{1}{2}$ cups
  4. D $2$ cups
Show answer and explanation

Correct answer: C - $4\frac{1}{2}$ cups

Writing $1\frac{1}{2}$ as $\frac{3}{2}$ gives $\frac{3}{2} \times 3 = \frac{9}{2} = 4\frac{1}{2}$ cups. The value $3\frac{1}{2}$ cups comes from adding $3$ instead of multiplying, $4\frac{1}{6}$ cups from tripling only the whole part and dividing the fraction, and $2$ cups from ignoring the number of cakes.

Q5
medium

Cloth costs ₹80 per metre. What is the cost of $2\frac{1}{2}$ metres?

  1. A ₹240
  2. B ₹82
  3. C ₹160
  4. D ₹200
Show answer and explanation

Correct answer: D - ₹200

Writing $2\frac{1}{2}$ as $\frac{5}{2}$ gives $\frac{5}{2} \times 80 = $ ₹200. The amount ₹160 pays for $2\ \text{m}$ only, ₹240 pays for $3\ \text{m}$, and ₹82 comes from adding instead of multiplying.

Q6
medium

In a class of $60$ students, $\frac{1}{3}$ play cricket and $\frac{1}{4}$ play football. No student plays both. How many students play one of these two games?

  1. A $25$
  2. B $35$
  3. C $15$
  4. D $20$
Show answer and explanation

Correct answer: B - $35$

Cricket has $60 \times \frac{1}{3} = 20$ students and football has $60 \times \frac{1}{4} = 15$, so together they number $35$. The values $20$ and $15$ each count only one game, and $25$ comes from taking a share of the wrong total.

Q7
medium

A farmer keeps $60$ hens, of which $\frac{2}{5}$ are white and the rest are brown. How many brown hens are there?

  1. A $30$
  2. B $36$
  3. C $12$
  4. D $24$
Show answer and explanation

Correct answer: B - $36$

Brown hens make up the other $\frac{3}{5}$, and one fifth of $60$ is $12$, so $12 \times 3 = 36$. The value $24$ counts the white hens, $12$ stops at one fifth, and $30$ is simply half the flock.

Q8
medium

A jar holds $\frac{3}{4}\ \text{kg}$ of sugar. First $\frac{1}{4}\ \text{kg}$ is used, and then half of what remains is used. How much sugar is left?

  1. A $\frac{3}{8}\ \text{kg}$
  2. B $\frac{1}{2}\ \text{kg}$
  3. C $\frac{1}{4}\ \text{kg}$
  4. D $\frac{1}{8}\ \text{kg}$
Show answer and explanation

Correct answer: C - $\frac{1}{4}\ \text{kg}$

After the first use, $\frac{3}{4} - \frac{1}{4} = \frac{1}{2}\ \text{kg}$ remains, and half of that is used, so $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\ \text{kg}$ is left. The value $\frac{1}{2}\ \text{kg}$ stops after the first step, $\frac{3}{8}\ \text{kg}$ halves the original amount, and $\frac{1}{8}\ \text{kg}$ halves twice over.

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