Arithmetic Quick Practice Quiz (Part 2): 20 Questions, WBPSC Clerkship 2024
A little practice. A step forward.
20 arithmetic questions for WBPSC Clerkship 2024, 30 seconds each, with explanations.
If the number 5x63 is divisible by 9, what is the value of x?
A number is divisible by 9 when the sum of its digits is a multiple of 9. Here 5 + x + 6 + 3 = 14 + x, and 18 is the multiple of 9 that fits, so x = 4. The other options give sums of 16, 20 or 22, none of which is a multiple of 9.
- Rule of 9: digit sum is a multiple of 9
- Rule of 3: digit sum is a multiple of 3
- 5463: 5+4+6+3 = 18
- Add the digits for 3 and 9.
What is the simple interest on ₹8,000 at 5% per annum for 3 years?
Simple interest = principal × rate × time ÷ 100 = 8000 × 5 × 3 ÷ 100 = ₹1,200. ₹1,500 is the interest on ₹10,000 for the same period, and ₹1,000 and ₹1,800 come from slips in multiplying.
- SI = P × R × T ÷ 100
- Amount = principal + interest
- Interest for one year: 8000 × 5 ÷ 100 = ₹400
- Find one year's interest first, then multiply by the years.
At 6% simple interest per annum, what sum earns ₹600 in 2 years?
Principal = interest × 100 ÷ (rate × time) = 600 × 100 ÷ (6 × 2) = 60000 ÷ 12 = ₹5,000. Check: 5000 × 6 × 2 ÷ 100 = 600.
- P = SI × 100 ÷ (R × T)
- You can check by putting the answer back
An article bought for ₹500 is sold for ₹600. What is the profit percent?
Profit = 600 − 500 = ₹100. Profit percent is always on the cost price: 100 ÷ 500 × 100 = 20%. Dividing by the selling price or a wrong base gives other figures such as 16 or 25.
- Profit% = profit ÷ cost price × 100
- Loss% = loss ÷ cost price × 100
- The base is always the cost price.
An article bought for ₹800 is sold for ₹720. What is the loss percent?
Loss = 800 − 720 = ₹80. Loss percent = 80 ÷ 800 × 100 = 10%. The other options come from using a wrong base.
- Loss = cost price − selling price
- The base is the cost price
The marked price of an article is ₹1,000. What is the selling price after a 20% discount?
Discount = 20% of 1000 = ₹200, so the selling price is 1000 − 200 = ₹800. ₹700 would be a 30% discount and ₹750 a 25% discount.
- Selling price = marked price − discount
- Discount is on the marked price
Convert a speed of 54 km per hour into metres per second.
To change km per hour into m per second, multiply by $\frac{5}{18}$. So 54 × $\frac{5}{18}$ = 15 m/s. Multiplying by $\frac{18}{5}$ by mistake gives a wrong result.
- km/h → m/s: $\times \frac{5}{18}$
- m/s → km/h: $\times \frac{18}{5}$
- 36 km/h = 10 m/s
- 1 km = 1000 m and 1 hour = 3600 s, and 1000 ÷ 3600 = $\frac{5}{18}$.
A 120 m long train crosses a pole in 12 seconds. What is its speed in km per hour?
To pass a pole the train covers a distance equal to its own length. Speed = 120 ÷ 12 = 10 m/s, and 10 × $\frac{18}{5}$ = 36 km/h.
- Crossing a pole: distance = length of the train
- m/s → km/h: $\times \frac{18}{5}$
How long does it take to travel 150 km at 50 km per hour?
Time = distance ÷ speed = 150 ÷ 50 = 3 hours.
- Time = distance ÷ speed
- Distance = speed × time
What is the average of the five numbers 12, 15, 18, 20 and 10?
Sum = 12 + 15 + 18 + 20 + 10 = 75. Average = 75 ÷ 5 = 15.
- Average = sum ÷ number of items
The average of 10 numbers is 20. If another number, 31, is added, what is the new average?
Old sum = 10 × 20 = 200. New sum = 200 + 31 = 231 and there are now 11 numbers, so the new average = 231 ÷ 11 = 21.
- Sum = average × count
- The divisor changes when a number is added
- Get the sum back from the average first.
A invests ₹6,000 and B invests ₹9,000 in a business and the profit after one year is ₹5,000. What is A's share?
The capitals are in the ratio 6000 : 9000 = 2 : 3 for the same time, so profit is shared 2 : 3. A's share = 5000 × $\frac{2}{5}$ = ₹2,000 and B gets ₹3,000.
- For equal time, profit is shared in the ratio of capital
- Reduce the ratio first
The perimeter of a square is 36 m. What is its area?
A square has four equal sides, so the side = 36 ÷ 4 = 9 m. Area = side × side = 9 × 9 = 81 sq m. The 36 is the perimeter, not the area.
- Perimeter of a square = 4 × side
- Area of a square = side × side
- Area of a rectangle = length × breadth
What is 12% of 250?
12% of 250 = 250 × 12 ÷ 100 = 30. Another way: 10% = 25 and 2% = 5, so the total is 30.
- p% of x = x × p ÷ 100
- 10% means one tenth
A number increased by 25% becomes 150. What is the number?
The new value is 125% of the original, so the number = 150 × 100 ÷ 125 = 120. Check: 25% of 120 = 30 and 120 + 30 = 150. Neither 125 nor 130 gives 150 after a 25% rise.
- Value after a rise = original × (100 + p) ÷ 100
- Original = new value × 100 ÷ (100 + p)
- Divide by 125%; do not subtract 25% from 150.
₹840 is divided in the ratio 5 : 7. What is the smaller share?
Total parts = 5 + 7 = 12 and one part = 840 ÷ 12 = ₹70. The smaller share = 5 × 70 = ₹350 and the larger = 7 × 70 = ₹490, which add up to 840.
- Total parts = sum of the ratio terms
- One part = total ÷ total parts
Express the recurring decimal $0.\overline{27}$ as a fraction.
With two repeating digits the fraction is the repeating part over 99, that is $\frac{27}{99}$. Dividing by 9 gives $\frac{3}{11}$. $\frac{27}{100}$ is the terminating decimal 0.27.
- One repeating digit: over 9
- Two repeating digits: over 99
- $0.\overline{3} = \frac{1}{3}$
What is the value of $\frac{3}{4} + \frac{5}{6}$?
The LCM of 4 and 6 is 12. $\frac{3}{4} = \frac{9}{12}$ and $\frac{5}{6} = \frac{10}{12}$, so the sum is $\frac{19}{12}$. Adding numerators and denominators separately gives $\frac{8}{10}$, which is wrong.
- Make the denominators equal before adding
- Use the LCM of the denominators
Which of these numbers is divisible by 11?
Rule of 11: the difference between the sums of digits in odd and even places must be 0 or a multiple of 11. For 3,245, (3 + 4) − (2 + 5) = 0, so it is divisible. The differences for 3,246, 3,254 and 3,425 are 1, 2 and 4, so none works. Check: 11 × 295 = 3,245.
- Rule of 11: difference of alternate digit sums is 0 or a multiple of 11
- 11 × 295 = 3,245
A traveller covers the first half of a journey at 40 km per hour and the second half, of equal distance, at 60 km per hour. What is the average speed in km per hour?
If each half is d, the total time is d ÷ 40 + d ÷ 60 = $\frac{d}{24}$, so the average speed = 2d ÷ $\frac{d}{24}$ = 48. By formula, $\frac{2xy}{x+y}$ = $\frac{2 \times 40 \times 60}{100}$ = 48. 50 is the plain mean of the two speeds, which is wrong here.
- Average speed for equal distances = $\frac{2xy}{x+y}$
- Average speed = total distance ÷ total time
- Total distance over total time, not the mean of the speeds.
📊 Topic Analysis
20 arithmetic questions for WBPSC Clerkship 2024, 30 seconds each, with explanations.
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