Arithmetic Quick Practice Quiz (Part 3): 20 Questions, WBPSC Clerkship 2024
A little practice. A step forward.
20 mixed arithmetic questions for WBPSC Clerkship 2024 Part-I.
If the four-digit number 53x4 is divisible by 9, what is the value of x?
For divisibility by 9 the sum of the digits must be a multiple of 9. Here 5 + 3 + x + 4 = 12 + x, which equals 18 when x = 6. With x = 3 the sum is 15 and with x = 7 it is 19, neither a multiple of 9. Check: 5364 ÷ 9 = 596.
- Divisible by 9 if the digit sum is a multiple of 9
- x is a single digit, so search 0–9
- Rule of 9: digit sum is 9
| Number | Rule |
|---|---|
| 9 | Sum of digits divisible by 9 |
| 3 | Sum of digits divisible by 3 |
| 11 | Difference of sums of alternate digits is 0 or a multiple of 11 |
What is the HCF of 48 and 72?
48 = $2^{4} \times 3$ and 72 = $2^{3} \times 3^{2}$. Taking the lowest power of each common prime, HCF = $2^{3} \times 3 = 24$. 12 and 18 divide both numbers but are not the greatest; 36 does not divide 48.
- HCF = product of common primes with the lowest powers
- The HCF divides every given number
What is the LCM of 12, 18 and 30?
12 = $2^{2} \times 3$, 18 = $2 \times 3^{2}$, 30 = $2 \times 3 \times 5$. Taking the highest power of every prime, LCM = $2^{2} \times 3^{2} \times 5 = 180$. 90 is not divisible by 12, while 360 and 540 are common multiples but not the least.
- LCM = product of all primes with their highest powers
- The LCM is a multiple of every given number
- HCF takes the lower power, LCM the higher
Express the recurring decimal $0.\overline{36}$ as a common fraction.
When two digits repeat, the denominator is 99: $0.\overline{36} = \frac{36}{99}$. Dividing by 9 gives $\frac{4}{11}$. $\frac{9}{25}$ is 0.36, a terminating decimal, not a recurring one.
- Two repeating digits give denominator 99
- Reduce by the common factor
- $0.36$ and $0.\overline{36}$ differ: $\frac{9}{25}$ versus $\frac{4}{11}$
- One repeating digit = 9, two = 99
Simplify: $15 + 6 \times (8 - 3) \div 2$
By BODMAS, brackets first: $8 - 3 = 5$. Then multiplication and division in order: $6 \times 5 = 30$, $30 \div 2 = 15$. Finally addition: $15 + 15 = 30$. Adding 15 + 6 before multiplying gives the wrong answer 52.5.
- BODMAS: brackets, orders, division, multiplication, addition, subtraction
- Multiplication and division rank equally, left to right
- Adding first gives the wrong answer 52.5
If ₹1,200 is divided in the ratio 3 : 5, what is the larger share?
The sum of the ratio is 3 + 5 = 8. The larger share is $\frac{5}{8} \times 1200 =$ ₹750 and the smaller is ₹450. ₹600 would be a 1 : 1 split and ₹720 a 3 : 2 split.
- Share = (own part ÷ sum of parts) × total
- Check that the shares add up: 450 + 750 = 1200
If 6 pens cost ₹90, what is the cost of 10 pens?
Cost of one pen = 90 ÷ 6 = ₹15. So 10 pens cost 15 × 10 = ₹150. More pens cost more, so this is direct proportion.
- Use the unitary method: find the value of one first
- Number of pens and total cost are directly proportional
What is 20% of 20% of 500?
20% of 500 = 100. Then 20% of 100 = 20. In one line, $500 \times \frac{20}{100} \times \frac{20}{100} = 20$. Taking only 20% of 500 (100) or 40% of 500 (200) gives other answers.
- Percentages can be applied one after another
- n% = $\frac{n}{100}$
The population of a town is 10,000. If it grows 10% every year, what will it be after 2 years?
After year one: 10,000 × 1.1 = 11,000. After year two: 11,000 × 1.1 = 12,100. Each year the increase is on the previous year's population, so simply adding 20% to get 12,000 is wrong.
- Compound growth: $P(1 + \frac{r}{100})^{n}$
- A 10% rise means multiplying by 1.1
- Two successive 10% rises make 21%, not 20%
What is the simple interest on ₹3,000 at 8% per annum for 2 years?
Simple interest = $\frac{P \times R \times T}{100} = \frac{3000 \times 8 \times 2}{100} =$ ₹480. The interest is the same every year, ₹240 a year. With compound interest the second year would earn slightly more.
- SI = PRT ÷ 100
- Amount = principal + interest = ₹3,480
At simple interest, a sum doubles in 10 years. What is the annual rate of interest?
Doubling means the interest equals the principal: $P = \frac{P \times R \times 10}{100}$, so $R = 10\%$. At 5% it would take 20 years and at 12.5% it would take 8 years.
- Doubling means interest = principal
- The sum doubles when R × T = 100
- Remember R × T = 100
An article bought for ₹800 is sold for ₹920. What is the profit percentage?
Profit = 920 − 800 = ₹120. Profit percent is always on the cost price: $\frac{120}{800} \times 100 = 15\%$. Taking it on the selling price would give about 13%, which is wrong.
- Profit % = (profit ÷ cost price) × 100
- Profit and loss percentages are on cost price
An article is sold at a 10% loss for ₹720. What is its cost price?
At a 10% loss the selling price is 90% of the cost price. So the cost price is $720 \div 0.9 =$ ₹800. ₹792 comes from adding 10% to ₹720, but the loss is on the cost price.
- A 10% loss means SP = 90% of CP
- CP = SP ÷ 0.9
- Adding 10% to 720 is the wrong route: the loss is on cost price
What is 54 km/h in metres per second?
To convert km/h to m/s multiply by $\frac{5}{18}$. $54 \times \frac{5}{18} = 15$ m/s. Dividing by 3.6 gives the same result.
- km/h to m/s: × $\frac{5}{18}$
- m/s to km/h: × $\frac{18}{5}$
- Multiply by 5, divide by 18
A 120 m long train moving at 12 m/s takes how long to cross a pole?
To pass a pole the train must cover its own length. Time = distance ÷ speed = 120 ÷ 12 = 10 seconds. The pole counts as a point, so its length is ignored.
- Crossing a pole: distance = length of the train
- Crossing a platform: train plus platform length
A person goes at 60 km/h and returns along the same route at 40 km/h. What is the average speed for the whole journey?
For equal distances the average speed is $\frac{2xy}{x + y} = \frac{2 \times 60 \times 40}{100} = 48$ km/h. The simple mean 50 km/h does not apply because more time is spent at the slower speed.
- Equal distances: average speed = $\frac{2xy}{x + y}$
- Average speed = total distance ÷ total time
- The simple mean of 60 and 40 is not the answer: the times are unequal
The area of a square is 144 square metres. What is its perimeter?
Side = $\sqrt{144} = 12$ m. Perimeter of a square = 4 × side = 4 × 12 = 48 m. A perimeter of 36 m would need a 9 m side, and 44 m or 52 m do not fit an area of 144 with a whole-number side.
- Area of a square = side × side
- Perimeter of a square = 4 × side
- Area is in square metres, perimeter in metres
What is the total cost of carpeting a room 8 m long and 5 m wide at ₹120 per square metre?
Area of the room = 8 × 5 = 40 square metres. Total cost = 40 × 120 = ₹4,800. Using the perimeter (26 m) would be wrong, because carpet covers area.
- Area of a rectangle = length × breadth
- Cost = area × rate per unit
A and B invest ₹6,000 and ₹9,000 respectively for the same period. If the profit is ₹7,500, what is B's share?
For equal time the profit is shared in the ratio of capital: 6000 : 9000 = 2 : 3. B's share = $\frac{3}{5} \times 7500 =$ ₹4,500 and A's share is ₹3,000. ₹3,000 is A's share, not B's, so check whose share is asked.
- Equal time: profit ratio = capital ratio
- Simplify the ratio first
- Writing A's share without checking whose share is asked is a common slip
Which of the following numbers is divisible by 11?
By the rule of 11, the difference between the sum of digits at odd places (2, 5) and even places (3, 4) must be 0 or a multiple of 11. For 2354, (2 + 5) − (3 + 4) = 0, so it is divisible: 2354 ÷ 11 = 214. For 2356 the difference is 2, for 2358 it is 4 and for 2360 it is 5.
- Rule of 11: difference of sums of alternate digits
- A difference of 0 also means divisible
| Number | Rule |
|---|---|
| 9 | Sum of digits divisible by 9 |
| 3 | Sum of digits divisible by 3 |
| 11 | Difference of sums of alternate digits is 0 or a multiple of 11 |
📊 Topic Analysis
20 mixed arithmetic questions for WBPSC Clerkship 2024 Part-I.
Leave a Comment
Commenting as ·