Sectional Test on Quantitative Techniques for CLAT UG [Part 4]
1. Six students scored an average of 75 marks in a test. One student’s marks were later found to be wrongly added and were actually 60 instead of 90. What is the correct average of the six students?
a. 70
b. 72
c. 75
d. 80
b. 72
c. 75
d. 80
2. A certain principal amount, when invested at a simple interest rate, grows to ₹12,000 in 4 years and to ₹15,000 in 8 years. Determine the initial principal amount.
a. ₹6000
b. ₹7500
c. ₹9000
d. ₹10,000
b. ₹7500
c. ₹9000
d. ₹10,000
3. If 10 workers can complete a project in 18 days, how many days will 15 workers take to complete the same project?
a. 10 days
b. 12 days
c. 14 days
d. 18 days
b. 12 days
c. 14 days
d. 18 days
4. A town had a population of 50,000 in the year 2019. In 2020, the population increased by 12%. In 2021, due to migration, the population decreased by 10%. What is the population of the town at the end of 2021?
a. 50,000
b. 54,000
c. 55,000
d. 55,400
b. 54,000
c. 55,000
d. 55,400
5. The ratio of teachers to students in a school is 1 : 20. If there are 420 students in the school, how many teachers are there?
a. 18
b. 20
c. 21
d. 22
b. 20
c. 21
d. 22
6. A bag’s marked price is set at ₹2,000 by a shopkeeper. Despite offering a 15% discount, the shopkeeper still achieves a 20% profit. Determine the original cost price of the bag.
a. ₹1,200
b. ₹1,250
c. ₹1,300
d. ₹1,360
b. ₹1,250
c. ₹1,300
d. ₹1,360
7. A bus makes a round trip between City A and City B. The outbound journey is completed at a speed of 60 km/h, and the return journey is at 40 km/h. If the entire trip lasts 10 hours, determine the distance separating the two cities.
a. 200 km
b. 240 km
c. 300 km
d. 360 km
b. 240 km
c. 300 km
d. 360 km
8. A rectangular field’s length is double its width. Given that its perimeter measures 180 meters, calculate the field’s area.
a. 1600 sq m
b. 1800 sq m
c. 2000 sq m
d. 2400 sq m
b. 1800 sq m
c. 2000 sq m
d. 2400 sq m
9. The ratio of the incomes of A and B is 5 : 7. If B earns ₹14,000 more than A, what is A’s income?
a. ₹30,000
b. ₹35,000
c. ₹40,000
d. ₹49,000
b. ₹35,000
c. ₹40,000
d. ₹49,000
10. From a box holding 6 red balls and 4 blue balls, a single ball is randomly selected. What is the probability that the chosen ball is red?
a. ⅕
b. ⅖
c. ⅗
d. ⅘
b. ⅖
c. ⅗
d. ⅘
11. The price of an article increases by 20% in the first year and decreases by 20% in the second year. What is the net change?
a. 4% decrease
b. 2% increase
c. 0%
d. 5% decrease
b. 2% increase
c. 0%
d. 5% decrease
12. A city authority planned a budget where 40% was to be spent on infrastructure, 35% on education, and the remaining amount on healthcare. If the total budget was ₹2 crore, how much money was allocated to healthcare?
a. ₹40 lakh
b. ₹45 lakh
c. ₹50 lakh
d. ₹55 lakh
b. ₹45 lakh
c. ₹50 lakh
d. ₹55 lakh
13. Two buses start at the same time from the same point and travel in opposite directions. One bus travels at 50 km/h and the other at 60 km/h. After how many hours will the distance between them be 330 km?
a. 3 hours
b. 6 hours
c. 2.5 hours
d. 5 hours
b. 6 hours
c. 2.5 hours
d. 5 hours
14. The average daily expenditure of a student over 6 days was ₹300. On one of the days, the student mistakenly recorded an expenditure of ₹500 instead of the actual ₹200. What is the correct average daily expenditure?
a. ₹275
b. ₹250
c. ₹300
d. ₹375
b. ₹250
c. ₹300
d. ₹375
15. A student buys 4 notebooks and 2 pens for a total of ₹180. Each notebook costs ₹30 more than a pen. What is the cost of one pen?
a. ₹10
b. ₹15
c. ₹20
d. ₹25
b. ₹15
c. ₹20
d. ₹25
Answers
- Correct Answer: A
Original total = 6 × 75 = 450
Excess added = 90 − 60 = 30
Correct total = 450 − 30 = 420
Average = 420 ÷ 6 = 70
- Correct Answer: C
Interest for 4 years = Amount at 8 years – Amount at 4 years = ₹15,000 – ₹12,000 = ₹3000
Since the interest for 4 years is ₹3000, the interest for a single year = ₹3000 / 4 years = ₹750 per year
The investment grew for 4 years to reach ₹12,000. The total interest in the first 4 years = ₹750 × 4 = ₹3000
The total amount after 4 years is the principal + the total interest earned.
₹12000 = Principal + ₹3000
Therefore, Principal = ₹12,000 – ₹3000 = ₹9000
- Correct Answer: B
Workers × Days = constant
10 × 18 = 15 × x
x = 12 days
- Correct Answer: D
2020 population = 50,000 × 1.12 = 56,000
2021 population = 56,000 × 0.9 = 55,440
- Correct Answer: C
1 teacher = 20 students
420 ÷ 20 = 21 teachers
- Correct Answer: B
Selling price after discount = 85% of 2000 = 1700
1700 = 120% of CP
CP = 1700/1.2 = ₹1,250
- Correct Answer: B
Let distance = d
d/60 + d/40 = 10
(2d + 3d)/120 = 10
5d = 1200
d = 240 km
- Correct Answer: C
Let breadth = x, length = 2x
Perimeter = 2(x + 2x) = 180
Perimeter = 2(x + 2x) = 180
6x = 180
x = 30
Area = 30 × 60 = 2,000
- Correct Answer: B
Difference = 7x – 5x = 14,000
2x = 14,000
x = 7000
A’s income = 5 × 7,000 = ₹35,000
- Correct Answer: C
Red balls = 6
Total balls = 10 (6 + 4)
Probability = 6/10 = ⅗
- Correct Answer: A
Net change = −(20 × 20)/100 = −4%
- Correct Answer: C
Spent on infrastructure + education = 40% + 35% = 75%
Remaining = 25%
25% of ₹2 crore = ₹50 lakh
- Correct Answer: A
Relative speed = 50 + 60 = 110 km/h
Time = 330/110 = 3 hours
14. Correct Answer: B
Recorded total = 6 × 300 = 1800
Extra added by mistake = 500 − 200 = 300
Correct total = 1800 − 300 = 1500
Correct average = 1500/6 = ₹250
15. Correct Answer: A
Let the cost of one pen be ₹x.
Then the cost of one notebook = ₹(x + 30).
Total cost = 4(x + 30) + 2x
= 4x + 120 + 2x
= 6x + 120
= 4x + 120 + 2x
= 6x + 120
Given total = 180
6x = 180 – 120
6x = 60
x = 10
6x = 60
x = 10
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Adtiya Aryan
Contributing author
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