Sectional Test on Quantitative Techniques for CLAT UG [Part 18]

1. The average of 12 numbers is 36. If the average of 8 numbers is 34, find the average of the remaining numbers.
a. 38
b. 40
c. 42
d. 44

2. A sum becomes ₹8,800 in 4 years and ₹9,600 in 5 years at simple interest. Find the rate of interest per year.
a. 8%
b. 10.5%
c. 14.28%
d. 15%

3. The ratio of two numbers is 5 : 7 and their sum is 144. Find the greater number.
a. 70
b. 72
c. 84
d. 96

4. A train running at 72 km/h crosses a platform 240 m long in 30 seconds. Find the length of the train.
a. 300 m
b. 360 m
c. 420 m
d. 480 m

5. If the cost price of 20 items equals the selling price of 16 items, find the profit percentage.
a. 20%
b. 25%
c. 30%
d. 35%

6. A number is increased by 20% and then decreased by 10%. What is the net percentage change?
a. 8% increase
b. 10% increase
c. 12% increase
d. 6% increase

7. A bag contains 4 red, 6 blue, and 10 green balls. What is the probability of selecting a blue ball?
a. 3/110
b. ⅕
c. ⅓
d. ⅖

8. A mixture of milk and water is in the ratio 4 : 3. If 7 litres of water are added, the ratio becomes 4 : 5. Find the original quantity of the mixture.
a. 28 L
b. 35 L
c. 42 L
d. 49 L

9. Two numbers are in the ratio 3 : 5 and their sum is 128. Find the smaller number.
a. 40
b. 45
c. 48
d. 52

10. A boat travels 24 km downstream in 3 hours and the same distance upstream in 4 hours. Find the speed of the boat in still water.
a. 6 km/h
b. 7 km/h
c. 8 km/h
d. 9 km/h

11. The side of a square is increased by 20%. By what percentage does the area increase?
a. 36%
b. 40%
c. 44%
d. 48%

12. The average of 10 numbers is 30. If each number is increased by 5, find the new average.
a. 32
b. 33
c. 34
d. 35

13. A trader marks his goods 25% above cost price and gives a discount of 10%. Find the profit percentage.
a. 10%
b. 12.5%
c. 15%
d. 20%

14. If the radius of a circle is increased by 20%, find the percentage increase in its area.
a. 40%
b. 42%
c. 44%
d. 48%

15. The present ages of A and B are in the ratio 3 : 4. After 5 years, their ratio becomes 4 : 5. Find A’s present age.
a. 12
b. 15
c. 18
d. 20

1. Correct Answer: B
Total = 12 × 36 = 432
Sum of 8 numbers = 8 × 34 = 272
Remaining sum = 432 − 272 = 160
Average = 160/4 = 40

2. Correct Answer: C
Difference = 9600 − 8800 = 800 (1 year interest)
Principal = 8800 − (4 × 800) = 5600
Rate = (800 × 100)/5600 = 14.28%

3. Correct Answer: C
Total parts = 12
1 part = 144/12 = 12
Greater number = 7 × 12 = 84

4. Correct Answer: B
Speed = 72 km/h = 20 m/s
Distance covered = 20 × 30 = 600 m
Train length = 600 − 240 = 360 m

5. Correct Answer: B
CP of 20 = SP of 16
CP/SP = 16/20 = ⅘
Profit = 25%

6. Correct Answer: A
100 × 1.20 = 120
120 × 0.90 = 108
Increase = (120-108) × 100 = 8% increase

7. Correct Answer: A
Blue balls = 6
Total = 20
Probability = 6/20 = 3/10

8. Correct Answer: B
Ratio change: 4:3 → 4:5
Water increases by 2 parts = 7 L
1 part = 3.5
Total parts = 7
Mixture = 7 × 5 = 35 L

9. Correct Answer: C
Total parts = 8
1 part = 128/8 = 16
Smaller = 3 × 16 = 48

10. Correct Answer: B
Downstream = 24/3 = 8
Upstream = 24/4 = 6
Boat speed = (8 + 6)/2 = 7 km/h

11. Correct Answer: C
Area factor = (1.2)² = 1.44
Increase = 44%

12. Correct Answer: D
Average increases by the same amount
30 + 5 = 35

13. Correct Answer: B
Marked price = 125
After 10% discount → 112.5
Profit = (125-112.5) × 100 = 12.5%

14. Correct Answer: C
Area ∝ r²
(1.2)² = 1.44
Increase = 44%

15. Correct Answer: B
Let ages = 3x, 4x
(3x + 5)/(4x + 5) = ⅘
Solve → x = 5
A = 3 × 5 = 15