Sub-Inspector of Statistics • 2026 • Paper-II
The ratio of A’s age to B’s age is 4:5. The ratio of their ages 6 years ago was 3:4. Find B’s present age.
A)
20 years
B)
24 years
C)
30 years
D)
34 years
Option C is correct: 30 years.
Sub-Inspector of Statistics • 2026 • Paper-II
The angle of elevation of the top of a tower from a point on the ground is 45°. If the point is 20 m away from the base of the tower, find the height of the tower.
A)
10 m
B)
20 m
C)
25 m
D)
15 m
Option B is correct: 20 m.
Sub-Inspector of Statistics • 2026 • Paper-II
A bag contains 5 white, 3 red, and 2 black balls. One ball is drawn at random. What is the probability that the ball drawn is neither white nor black?
A)
1/5
B)
3/10
C)
2/5
D)
1/2
Option B is correct: 3/10.
Sub-Inspector of Statistics • 2026 • Paper-II
The surface area of a cube is 150 cm2. Its volume is:
A)
125 cm3
B)
64cm3
C)
150 cm3
D)
216 cm3
Option A is correct: 125 cm3.
Sub-Inspector of Statistics • 2026 • Paper-II
A shopkeeper bought a bag for 800 and sold it for 1000. His gain percent is:
A)
20%
B)
22%
C)
25%
D)
30%
Option C is correct: 25%.
Sub-Inspector of Statistics • 2026 • Paper-II
A cyclist covers 750 metres in 2 min 30 sec. His speed in km/hr is:
A)
18 km/hr
B)
15 km/hr
C)
12.5 km/hr
D)
10 km/hr
Option A is correct: 18 km/hr.
Sub-Inspector of Statistics • 2026 • Paper-II
The mean of 20 observations is 30. Later it was found that one value 20 was wrongly taken instead of 40. Find the correct mean.
A)
29
B)
30
C)
31
D)
32
Option C is correct: 31.
Sub-Inspector of Statistics • 2026 • Paper-II
The smallest number by which 180 must be multiplied to make it a perfect square is:
A)
2
B)
3
C)
10
D)
5
Option D is correct: 5.
Sub-Inspector of Statistics • 2026 • Paper-II
Zama travels from Aizawl to Tlungvel at a speed of 40 km/hr and returns to Aizawl by increasing his speed by 50%. What is his average speed?
A)
36 km/hr
B)
45 km/hr
C)
48 km/hr
D)
30 km/hr
Step-by-step solution:
1. **Identify the speed for the first leg (Aizawl to Tlungvel):**
Speed 1 (v1) = 40 km/hr.
2. **Calculate the speed for the return leg (Tlungvel to Aizawl):**
The speed is increased by 50%.
Increase = 50% of 40 = 20 km/hr.
Speed 2 (v2) = 40 + 20 = 60 km/hr.
3. **Apply the Average Speed Formula:**
When a person travels the same distance (d) at two different speeds (v1 and v2), the average speed is the harmonic mean of the speeds, given by the formula:
Average Speed = (2 * v1 * v2) / (v1 + v2)
4. **Substitute the values:**
Average Speed = (2 * 40 * 60) / (40 + 60)
Average Speed = 4800 / 100
Average Speed = 48 km/hr.
Conclusion: Option (c) is correct. Options (a), (b), and (d) are incorrect as they do not follow the harmonic mean calculation required for equal-distance round trips.
Sub-Inspector of Statistics • 2026 • Paper-II
cos 28° sin 62° + sin 28° cos 62° =
A)
0
B)
1/2
C)
1
D)
sin 34°
Option C is correct: 1.
Sub-Inspector of Statistics • 2026 • Paper-II
The distance of the point (-8,6) from the origin is:
A)
5 units
B)
2√2 units
C)
2 units
D)
10 units
Option D is correct: 10 units.
Sub-Inspector of Statistics • 2026 • Paper-II
The LCM of (2x^3 - 5x^2 - 3x) and (x^4 - 27x) is
A)
x(x^2 + 3x + 9)(2x + 1)(x + 3)
B)
x(x^2 + 3x + 9)(2x + 1)(x - 3)
C)
(x^2 + 3x + 9)(2x + 1)(x - 3)
D)
(x^2 + 3x + 9)(2x + 1)(x + 3)
Option B is correct: x(x^2 + 3x + 9)(2x + 1)(x - 3).
Sub-Inspector of Statistics • 2026 • Paper-II
A train 200 m long is running at a speed of 90 km/hr. Find the time it takes to pass a platform 100 metres long.
A)
8 seconds
B)
10 seconds
C)
12 seconds
D)
15 seconds
Option C is correct: 12 seconds.
Sub-Inspector of Statistics • 2026 • Paper-II
A shirt is marked at 600 and sold at 510. The discount percentage is:
A)
10%
B)
20%
C)
12%
D)
15%
Option D is correct: 15%.
Sub-Inspector of Statistics • 2026 • Paper-II
The cost of 21 pens and 9 notebooks is Rs. 819. The cost of 7 pens and 3 notebooks is:
A)
204
B)
409
C)
273
D)
208
Option C is correct: 273.
Sub-Inspector of Statistics • 2026 • Paper-II
A car goes 120 km at 60 km/hr and returns 120 km at 40 km/hr. Average speed is:
A)
48 km/hr
B)
50 km/hr
C)
52 km/hr
D)
54 km/hr
Option A is correct: 48 km/hr.
Sub-Inspector of Statistics • 2026 • Paper-II
A rectangular floor of 18 m × 12 m is to be tiled with square tiles of side 3 m. A rectangular platform of 12 m × 6 m is built in the centre and left untiled. Find the number of tiles required.
A)
12
B)
14
C)
16
D)
none of these
Option C is correct: 16.
Sub-Inspector of Statistics • 2026 • Paper-II
The ratio of milk to water in 80 litres of a mixture is 7:3, the amount of water (in litres) to be added to the mixture to make the ratio 2:1 is:
A)
4
B)
5
C)
6
D)
7
Option A is correct: 4.
Sub-Inspector of Statistics • 2026 • Paper-II
The capacity of two pots is 70 litres and 105 litres respectively. Find the capacity of a container which can exactly measure the contents of the two pots.
A)
25 litres
B)
58 litres
C)
35 litres
D)
18 litres
Option C is correct: 35 litres.
Sub-Inspector of Statistics • 2026 • Paper-II
If 18% of a number is 27, find 30% of that number.
A)
45
B)
40
C)
44
D)
none of these
Option A is correct: 45.
Sub-Inspector of Statistics • 2026 • Paper-II
A wire is bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, its area will be:
A)
2288 cm2
B)
8822 cm2
C)
4477 cm2
D)
7744 cm2
Option D is correct: 7744 cm2.
Sub-Inspector of Statistics • 2026 • Paper-II
If the SP of an item is Rs. 21 for 30% discount on list price, then what would be the SP for 20% discount on list price?
A)
20
B)
24
C)
22
D)
25
Option B is correct: 24.
Sub-Inspector of Statistics • 2026 • Paper-II
A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of the probability of drawing a red ball, find the number of blue balls in the bag.
A)
15
B)
12
C)
17
D)
11
Option A is correct: 15.
Sub-Inspector of Statistics • 2026 • Paper-II
The marked price of a refrigerator is 20,000. A shopkeeper gives a 15% discount and charges 10% sales tax on the discounted price. Find the net amount paid by the customer.
A)
17,800
B)
19,800
C)
18,700
D)
20,000
Option C is correct: 18,700.
Sub-Inspector of Statistics • 2026 • Paper-II
Which is the first Indian state to implement one paid menstrual leave day per month for women in Government and Private sector?
A)
Odisha
B)
Nagaland
C)
Karnataka
D)
Kerala
Option A is correct: Odisha.
