Sectional Test on Quantitative Techniques for CLAT UG [Part 14]

1. The average of 12 numbers is 28. If the average of 5 of them is 20 and the average of 4 others is 32, find the average of the remaining numbers.
a. 30
b. 32
c. 34
d. 36

2. A sum becomes ₹6,600 in 3 years and ₹7,200 in 4 years at simple interest. Find the principal.
a. ₹4,200
b. ₹4,800
c. ₹5,400
d. ₹6,000

3. The ratio of two numbers is 9 : 7 and their difference is 30. Find the larger number.
a. 105
b. 135
c. 150
d. 165

4. A train travels 240 km. If the train’s speed were 20 km/h faster, the journey time would decrease by 2 hours. What was the train’s initial speed?
a. 40 km/h
b. 48 km/h
c. 60 km/h
d. 72 km/h

5. If the cost price of 18 items equals the selling price of 15 items, what is the profit percentage?
a. 15%
b. 18%
c. 20%
d. 25%

6. A number increased by 25% and then decreased by 20%. What is the net change?
a. 5% increase
b. No change
c. 5% decrease
d. 10% increase

7. A bag contains 8 red, 6 blue, and 6 green balls. What is the probability of drawing a blue ball?
a. ⅕
b. ¼
c. 3/10
d. ⅖

8. A mixture contains milk and water in a 5:4 ratio. When 12 liters of water are added, the ratio changes to 5:7. Determine the initial volume of the mixture.
a. 36 litres
b. 45 litres
c. 54 litres
d. 63 litres

9. Two numbers are in the ratio 4 : 9. Their sum is 91. Find the smaller number.
a. 21
b. 28
c. 35
d. 42

10. A boat travels 30 km with the current in 3 hours, but the return journey against the current takes 5 hours. What is the velocity of the water current?
a. 2 km/h
b. 3 km/h
c. 4 km/h
d. 5 km/h

11. The side of a square is increased by 10%. By what percentage does its area increase?
a. 10%
b. 20%
c. 21%
d. 25%

12. Out of 15 students with an average age of 18 years, five students have an average age of 16 years, and another five have an average age of 20 years. What is the average age of the remaining students?
a. 17
b. 18
c. 19
d. 20

13. A man saves 30% of his income. If his savings are ₹9,000, what is his income?
a. ₹25,000
b. ₹27,000
c. ₹30,000
d. ₹32,000

14. If the radius of a circle is increased by 20%, by what percentage does the area increase?
a. 36%
b. 40%
c. 44%
d. 48%

15. A’s and B’s current ages are in the proportion of 3 to 5. Six years from now, this ratio will change to 4 to 6. Determine A’s current age.
a. 18
b. 24
c. 30
d. 36

2. Correct Answer: D
1 year interest = 7200 − 6600 = 600
4 years interest = 2400
Principal = 7200 − 2400 = ₹6000

3. Correct Answer: B
Difference = 2 parts = 30
1 part = 15
Larger = 9×15 = 135

4. Correct Answer: C
Let speed = x
240/x − 240/(x+20) = 2
x = 60 km/h

5. Correct Answer: C
Let CP per item = 1
CP of 18 = 18
SP per item = 18/15 = 1.2
Profit = 20%

6. Correct Answer: B
1.25 × 0.8 = 1
No change

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

8. Correct Answer: A
Water increases from 4 parts to 7 parts → increase = 3 parts
3 parts = 12 litres → 1 part = 4 litres
Original parts = 5 + 4 = 9
Original quantity = 9 × 4 = 36 litres

9. Correct Answer: B
Total parts = 13
1 part = 7
Smaller = 4×7 = 28

10. Correct Answer: A
Downstream = 10 km/h
Upstream = 6 km/h
Stream = (10−6)/2 = 2 km/h

11. Correct Answer: C
Area ↑ = (1.1)² − 1 = 21%

12. Correct Answer: B
Total = 15×18 = 270
Known = (5×16 + 5×20) = 180
Remaining sum = 90
Average = 90/5 = 18

13. Correct Answer: C
30% = 9000
Income = 9000 × 100 / 30 = ₹30,000

14. Correct Answer: C
Area ↑ = (1.2)² − 1 = 44%

15. Correct Answer: B
Let ages = 3x and 5x
(3x+6)/(5x+6) = 4/6
x = 8
A = 3×8 = 24