SSC CGL 20 September 2025 · Shift 3 · Quantitative Aptitude — questions with answers · ShikshaSphere
Chapter 107 of 192
20 September 2025 · Shift 3
Quantitative Aptitude
25 questions ~25 min readFree
25 questions
A
51
Find the value of x in the given equation:
= 5
A.
B.
C.
D.
Solution
Componendo–dividendo
Let a = and b = ; then = 5 ⇒ a + b = 5a − 5b ⇒ = .
Squaring: = .
32 + 4x = 72 − 9x ⇒ 13x = 40.
x = — option (c).
52
How much will the compound interest on ₹24,000 at 20% per annum for 9 months be, if it is compounded quarterly?
A.₹3,222
B.₹3,422
C.₹1,622
D.₹3,783
Solution
CI compounded quarterly
Quarterly compounding makes the rate = 5% per quarter.
9 months contain 3 such quarters.
Amount = 24,000(1.05)³ = 24,000 × 1.157625 = ₹27,783.
CI = 27,783 − 24,000 = ₹3,783 — option (d).
53
15 women can do a work in 14 days. 30 men can complete the same work in 10 days. What is the ratio between the efficiency of a man and a woman?
A.7 : 10
B.8 : 4
C.7 : 9
D.10 : 9
Solution
Man : woman efficiency
The same work is done either way: 15 × 14 women-days = 30 × 10 men-days.
210W = 300M, where W and M are one-day outputs.
= = .
M : W = 7 : 10 — option (a).
54
Which of the following numbers is an integer but NOT a natural number?
A.2
B.0
C.7
D.9
Solution
Integer but not natural
Natural numbers begin from 1: 1, 2, 3, …
Integers include 0 and the negatives as well.
0 is an integer but is not counted among the natural numbers.
Hence option (b).
55
Naveen covers half of his journey at 18 km/h and the remaining half at 9 km/h. His average speed is:
A.12 km/h
B.11 km/h
C.14 km/h
D.13 km/h
Solution
Average speed
For equal halves the average speed is the harmonic mean.
Average = .
= .
= 12 km/h — option (a).
56
A hemisphere is inscribed in a cube of side 12 cm. What is the volume of the hemisphere?
A.356.55 cm³
B.354.24 cm³
C.350.26 cm³
D.452.16 cm³
Solution
Hemisphere in a cube
The flat face of the hemisphere fits the cube’s face, so its diameter equals the side, 12 cm.
Radius = = 6 cm.
Volume = πr³ = × 3.14 × 216.
= 452.16 cm³ — option (d).
57
A bus travels 11.9 km using 1.4 litres of fuel. How many kilometres does it travel per litre?
A.8.25 km
B.8.5 km
C.8.75 km
D.8.0 km
Solution
Mileage
Mileage = .
= .
= .
= 8.5 km per litre — option (b).
58
A venture has three stakeholders. P brought 60% of the capital and Q brought the rest. R joined later and was promised 30% of the total profit for branding. If the total profit was ₹3,50,000, how much was Q's share?
A.₹84,000
B.₹90,000
C.₹98,000
D.₹1,05,000
Solution
Profit with a third partner
R's share = 3,50,000 × = ₹1,05,000.
Remaining profit = 3,50,000 − 1,05,000 = ₹2,45,000, split between P and Q as 60 : 40 = 3 : 2.
Q gets of ₹2,45,000.
= ₹98,000 — option (c).
59
A vessel contains milk and water in the ratio 6 : 5. If 10 litres of milk are removed and 9 litres of water are added, the new ratio becomes 2 : 3. What was the original quantity of the mixture in the vessel?
A.67 L
B.66 L
C.68 L
D.78 L
Solution
Mixture — remove and add
Let milk = 6x and water = 5x, so the total is 11x.
= ⇒ 18x − 30 = 10x + 18.
8x = 48 ⇒ x = 6.
Total = 11 × 6 = 66 L — option (b).
60
A triangular window has an area equal to 35% of a square window of area 300 m². If its base is 20 m, find its height.
A.12.5 m
B.18.6 m
C.10.5 m
D.24.5 m
Solution
Triangle area
Area of the triangle = 300 × = 105 m².
Area = × base × height ⇒ 105 = × 20 × h.
10h = 105.
h = 10.5 m — option (c).
61
P and Q can complete a task in 18 days together. P is 20% more efficient than Q. What percentage of the work is done by P alone?
A.54.54%
B.60.6%
C.62.5%
D.66.66%
Solution
Efficiency share
P is 20% more efficient, so P : Q = 120 : 100 = 6 : 5.
Together they represent 6 + 5 = 11 parts of the work.
P’s share = × 100.
= 54.54% — option (a).
62
A businessman invests ₹40,000 in buying a bike and spends ₹8,000 on transportation and ₹7,000 on storage. If he sells the bike for ₹60,000, what is the profit or loss percentage?
A.9.09% profit
B.8.42% loss
C.8.26% loss
D.5.26% profit
Solution
Profit with extra costs
Total cost = 40,000 + 8,000 + 7,000 = ₹55,000.
Selling price = ₹60,000, so profit = ₹5,000.
Profit% = × 100.
= 9.09% profit — option (a).
63
Rahul can do a piece of work in 12 days and Pawan can do it in 15 days. If they work together for 2 days, how much of the work will be left?
A.
B.
C.
D.
Solution
Work left
Take the work as LCM(12, 15) = 60 units ⇒ Rahul 5/day, Pawan 4/day.
In 2 days together: 2 × 9 = 18 units.
Left = 60 − 18 = 42 units.
Fraction left = = — option (a).
64
A train covered a certain distance in 3 parts with average speeds of 12 km/h, 15 km/h and 30 km/h. What is the average speed over the entire journey, assuming equal distances?
A.12.05 km/h
B.16.36 km/h
C.19.09 km/h
D.16.25 km/h
Solution
Average speed — three parts
Take each part as LCM(12, 15, 30) = 60 km, so the total distance is 180 km.
Times: = 5, = 4 and = 2 hours — total 11 hours.
Average = .
= 16.36 km/h — option (b).
65
A display stand is shaped like a right triangular prism. The triangular base is a right-angled triangle with perpendicular sides measuring 8 cm and 15 cm. The height of the prism is 5 cm. What is the ratio of the area of the largest rectangular face to the area of the smallest rectangular face?
A.13 : 8
B.17 : 8
C.15 : 13
D.5 : 14
Solution
Prism faces ratio
(8, 15, 17) is a Pythagorean triplet, so the third side is 17 cm.
Each rectangular face = triangle side × prism height: 8×5 = 40, 15×5 = 75 and 17×5 = 85 cm².
Largest = 85, smallest = 40.
Ratio = 85 : 40 = 17 : 8 — option (b).
66
In a 60-litre mixture of apple juice and water, the amount of water is 20 litres. How many litres of water should be added to make the ratio of juice to water 2 : 3?
A.50 L
B.30 L
C.40 L
D.80 L
Solution
Add water to change ratio
Juice = 60 − 20 = 40 L; water = 20 L. The juice stays fixed.
= ⇒ 120 = 40 + 2x.
2x = 80.
x = 40 L — option (c).
67
If sinA = and A is acute, then what is the value of cosA?
A.
B.
C.
D.
Solution
cosA from sinA
(5, 12, 13) is a Pythagorean triplet, so the base is 12.
cosA = .
= .
Hence option (a).
68
If a line passes through (4, −1) with slope 6, find the y-intercept.
A.−23
B.−25
C.24
D.−12
Solution
y-intercept
Write y = mx + c with m = 6.
Put the point: −1 = 6(4) + c.
c = −1 − 24.
c = −25 — option (b).
69
Two parallel lines are intersected by a transversal. If a pair of corresponding angles is formed and one of the angles measures 100°, what is the measure of the other angle?
A.60°
B.90°
C.100°
D.150°
Solution
Corresponding angles
When a transversal cuts two parallel lines, corresponding angles are EQUAL.
One of them is 100°.
So the other is also 100°.
Hence option (c).
70
If △PQR ∼ △MNO and ∠P = 70°, ∠Q = 80°, then ∠N = ?
A.70°
B.80°
C.50°
D.Cannot be determined
Solution
Similar triangles — angles
In similar triangles the corresponding angles are equal.
The order P↔M, Q↔N, R↔O gives ∠N = ∠Q.
∠Q = 80°.
So ∠N = 80° — option (b).
A circle has two chords, each 8 cm long. If one chord is 2 cm away from the centre, what is the distance of the other chord from the centre?
A.1 cm
B.2 cm
C.3 cm
D.4 cm
Solution
Equal chords
Chords of equal length in the same circle are equidistant from the centre.
Both chords measure 8 cm.
So the second is also 2 cm from the centre.
Hence option (b).
73
From an external point X, two tangents are drawn to a circle, touching it at M and N. The chord of contact MN subtends an angle α at the centre O. What is the angle ∠MXN between the tangents in terms of α?
A.α
B.2α
C.180° − α
D.90° − α
Solution
Angle between tangents
OM and ON are perpendicular to the tangents, so ∠OMX = ∠ONX = 90°.
In quadrilateral OMXN the four angles add to 360°.
90° + 90° + α + ∠MXN = 360°.
∠MXN = 180° − α — option (c).
74
If sinA = , find the value of sin⁴A + cos⁴A.
A.
B.
C.
D.
Solution
sin⁴A + cos⁴A
(3, 4, 5) is a Pythagorean triplet, so cosA = .
sin⁴A = ()⁴ = and cos⁴A = ()⁴ = .
Adding: .
= — option (a).
75
Add: 8.65 + 9.28 + 0.067
A.11.257
B.8.867
C.7.768
D.17.997
Solution
Decimal addition
Line up the decimal points: 8.650 + 9.280 + 0.067.
8.650 + 9.280 = 17.930.
17.930 + 0.067.
= 17.997 — option (d).
Finished reading? Now test yourself.
The same 25 questions, but with a timer and the answers hidden — 15 minutes.
Let a = and b = ; then = 5 ⇒ a + b = 5a − 5b ⇒ = .
Squaring: = .
32 + 4x = 72 − 9x ⇒ 13x = 40.
x = — option (c).
Quarterly compounding makes the rate = 5% per quarter.
9 months contain 3 such quarters.
Amount = 24,000(1.05)³ = 24,000 × 1.157625 = ₹27,783.
CI = 27,783 − 24,000 = ₹3,783 — option (d).
The same work is done either way: 15 × 14 women-days = 30 × 10 men-days.
210W = 300M, where W and M are one-day outputs.
= = .
M : W = 7 : 10 — option (a).
For equal halves the average speed is the harmonic mean.
Average = .
= .
= 12 km/h — option (a).
The flat face of the hemisphere fits the cube’s face, so its diameter equals the side, 12 cm.
Radius = = 6 cm.
Volume = πr³ = × 3.14 × 216.
= 452.16 cm³ — option (d).
R's share = 3,50,000 × = ₹1,05,000.
Remaining profit = 3,50,000 − 1,05,000 = ₹2,45,000, split between P and Q as 60 : 40 = 3 : 2.
Q gets of ₹2,45,000.
= ₹98,000 — option (c).
Let milk = 6x and water = 5x, so the total is 11x.
= ⇒ 18x − 30 = 10x + 18.
8x = 48 ⇒ x = 6.
Total = 11 × 6 = 66 L — option (b).
Area of the triangle = 300 × = 105 m².
Area = × base × height ⇒ 105 = × 20 × h.
10h = 105.
h = 10.5 m — option (c).
P is 20% more efficient, so P : Q = 120 : 100 = 6 : 5.
Together they represent 6 + 5 = 11 parts of the work.
P’s share = × 100.
= 54.54% — option (a).
Total cost = 40,000 + 8,000 + 7,000 = ₹55,000.
Selling price = ₹60,000, so profit = ₹5,000.
Profit% = × 100.
= 9.09% profit — option (a).
Take each part as LCM(12, 15, 30) = 60 km, so the total distance is 180 km.
Times: = 5, = 4 and = 2 hours — total 11 hours.
Average = .
= 16.36 km/h — option (b).
(8, 15, 17) is a Pythagorean triplet, so the third side is 17 cm.
Each rectangular face = triangle side × prism height: 8×5 = 40, 15×5 = 75 and 17×5 = 85 cm².
Largest = 85, smallest = 40.
Ratio = 85 : 40 = 17 : 8 — option (b).
Juice = 60 − 20 = 40 L; water = 20 L. The juice stays fixed.
= ⇒ 120 = 40 + 2x.
2x = 80.
x = 40 L — option (c).
(5, 12, 13) is a Pythagorean triplet, so the base is 12.
cosA = .
= .
Hence option (a).
When a transversal cuts two parallel lines, corresponding angles are EQUAL.
One of them is 100°.
So the other is also 100°.
Hence option (c).
Chords of equal length in the same circle are equidistant from the centre.
Both chords measure 8 cm.
So the second is also 2 cm from the centre.
Hence option (b).
OM and ON are perpendicular to the tangents, so ∠OMX = ∠ONX = 90°.
In quadrilateral OMXN the four angles add to 360°.
90° + 90° + α + ∠MXN = 360°.
∠MXN = 180° − α — option (c).
(3, 4, 5) is a Pythagorean triplet, so cosA = .
sin⁴A = ()⁴ = and cos⁴A = ()⁴ = .
Adding: .
= — option (a).