Percentages, Ratio and Averages — Practice Questions
CSAT-pattern practice on percentages, ratio and averages — base change, successive change, combined ratios, averages, alligation and percentage points, fully worked.
Questions
These are original CSAT-pattern practice questions written for this site — not past UPSC papers. No calculator; target time about 8 minutes.
A’s salary is 25% more than B’s salary. By what percentage is B’s salary less than A’s?
Solution
Let B $= 100$, so A $= 125$. B is 25 less than A, and the base is now A:
$$\frac{25}{125} \times 100 = 20\%$$The tempting 25% uses the wrong base.
Answer: C
The population of a town increases by 10% in one year and decreases by 10% in the next year. If the present population is 50,000, what will it be after two years?
Solution
Net change $= 10 - 10 + \dfrac{10 \times (-10)}{100} = -1\%$.
Population $= 50{,}000 \times 0.99 = 49{,}500$. (Directly: $50{,}000 \to 55{,}000 \to 49{,}500$.)
Answer: D
An amount of ₹2,100 is divided among A, B and C such that $A : B = 2 : 3$ and $B : C = 4 : 5$. What is C’s share?
Solution
Equalise B ($\text{LCM}(3, 4) = 12$): $A : B = 8 : 12$, $B : C = 12 : 15$ → $A : B : C = 8 : 12 : 15$ (35 parts).
One part $= 2{,}100 \div 35 = 60$. C $= 15 \times 60 = ₹900$.
Check: A $= 480$, B $= 720$, C $= 900$; total $2{,}100$ ✓.
Answer: C
The average age of 30 students in a class is 15 years. When the teacher’s age is included, the average increases by 1 year. What is the teacher’s age?
Solution
Students’ total $= 30 \times 15 = 450$. With the teacher: $31 \times 16 = 496$. Teacher $= 496 - 450 = 46$ years.
Shortcut: teacher $=$ new average $+$ (number of students × increase) $= 16 + 30 \times 1 = 46$.
Answer: C
A shopkeeper mixes two varieties of pulses costing ₹60 per kg and ₹90 per kg. In what ratio should they be mixed to obtain a mixture worth ₹72 per kg?
Solution
Alligation: cheaper : dearer $= (90 - 72) : (72 - 60) = 18 : 12 = 3 : 2$.
Check: $\dfrac{3 \times 60 + 2 \times 90}{5} = \dfrac{360}{5} = 72$ ✓.
Answer: A
The unemployment rate in a region rises from 5% to 6%. Consider the following statements:
- The rate has risen by 1 percentage point.
- The rate has risen by 20 per cent.
- The rate has risen by 1 per cent.
Which of the statements given above is/are correct?
Solution
- Absolute change $= 6 - 5 = 1$ percentage point → statement 1 correct.
- Relative change $= \dfrac{1}{5} \times 100 = 20$ per cent → statement 2 correct.
- Statement 3 confuses the two → wrong.
Answer: B