SSC CGL 24 September 2025 · Shift 1 · Quantitative Aptitude — questions with answers · ShikshaSphere
Chapter 147 of 192
24 September 2025 · Shift 1
Quantitative Aptitude
25 questions ~25 min readFree
25 questions
A
51
Simplify:
A.2 + 3
B.2 +
C. +
D.2 +
Solution
Nested surd
Write 11 as 8 + 3 and 4 as 2.
So 11 + 4 = ( + )².
Taking the square root gives + .
= 2 + — option (b).
52
A sum of ₹10,000 is lent out in two parts, one at 4% simple interest and the other at 6% simple interest. If the annual interest is ₹520, the sum lent at 4% is:
A.₹7,200
B.₹5,500
C.₹6,000
D.₹4,000
Solution
Two-part simple interest
Overall rate = × 100 = 5.2%.
By alligation: (6 − 5.2) : (5.2 − 4) = 0.8 : 1.2 = 2 : 3.
So the 4% part is of the total.
× 10,000 = ₹4,000 — option (d).
53
Rajesh covers one-third of his journey at a speed of 10 km/h, the next one-third at 20 km/h and the remaining part at 60 km/h. What is his average speed?
A.32 km/h
B.24 km/h
C.18 km/h
D.20 km/h
Solution
Average speed
Take the total distance as D; each part is .
Total time = + + = = .
Average speed = = .
= 18 km/h — option (c).
54
A man observes the top of a tower at an angle of elevation of 30°. He walks 20 metres towards the tower and the angle of elevation becomes 45°. What is the height of the tower?
A.10( + 1) m
B.10( + 3) m
C.15( + 1) m
D.15(3 + ) m
Solution
Angle of elevation
Let the height be h. At 45° the distance from the foot equals h.
At 30° the distance is h + 20, and tan30° = = .
h = h + 20 ⇒ h( − 1) = 20 ⇒ h = .
Rationalising: h = 10( + 1) m — option (a).
55
A rectangular tank measures 15 cm long, 14 cm wide and 9 cm high. If a spherical ball of the largest possible size is placed inside this tank, what is the volume of the space not occupied by the ball?
A.(1790 − 121.5π) cm³
B.(1880 − 121.5π) cm³
C.(1999 − 121.5π) cm³
D.(1890 − 121.5π) cm³
Solution
Sphere in a box
Tank volume = 15 × 14 × 9 = 1890 cm³.
The largest ball is limited by the SMALLEST dimension, 9 cm, so its radius is 4.5 cm.
Ball volume = π(4.5)³ = 121.5π cm³.
Empty space = (1890 − 121.5π) cm³ — option (d).
56
P and Q share profit in the ratio 9 : 7. If P gets ₹27,000, how much did Q receive?
A.₹21,500
B.₹10,000
C.₹21,000
D.₹22,000
Solution
Profit sharing
P’s 9 parts equal ₹27,000.
So 1 part = = ₹3,000.
Q has 7 parts = 7 × 3,000.
= ₹21,000 — option (c).
57
What is the ratio of the interior angle of a regular pentagon to the interior angle of a regular decagon?
Mohit walks around a square plot of area 196 m². If he walks once around its boundary, how far does he walk?
A.59 m
B.52 m
C.47 m
D.56 m
Solution
Perimeter of a square
Area = side², so side = = 14 m.
Perimeter = 4 × side.
= 4 × 14.
= 56 m — option (d).
59
Two numbers are in the ratio 8 : 9. If 8 is added to each, the new ratio becomes 17 : 19. What are the original numbers?
A.143 and 179
B.128 and 144
C.115 and 137
D.136 and 152
Solution
Ratio with addition
Let the numbers be 8x and 9x.
= ⇒ 19(8x + 8) = 17(9x + 8).
152x + 152 = 153x + 136 ⇒ x = 16.
The numbers are 128 and 144 — option (b).
60
P : Q = 2 : 3, Q : R = 6 : 5 and R : S = 10 : 7. What is the ratio P : S?
A box contains 25% yellow balls, 40% purple balls and the rest are green. If there are 70 green balls, what is the total number of balls?
A.150
B.205
C.200
D.180
Solution
Percentage of a total
Green share = 100% − 25% − 40% = 35%.
35% of the total = 70.
Total = .
= 200 — option (c).
62
A student answered 80% of the questions in an examination. He answered 75% of the answered questions correctly, and he was also given grace marks for 25% of the questions he did not answer. If the total number of questions is 180, how many questions did he get correct (including grace)?
A.137
B.117
C.108
D.145
Solution
Answered, correct, grace
Questions answered = 180 × = 144.
Correct among them = 144 × = 108.
Unanswered = 180 − 144 = 36, and grace on 25% of these = 9.
Total = 108 + 9 = 117 — option (b).
63
A trader gave a 25% discount on the marked price but still earned a 15% profit. What percentage was the marked price above the cost price?
A cricketer has played 10 innings with an average score of 50. In the next innings he scores 110. What will be the new average?
A.50.45
B.66.33
C.55.45
D.49.45
Solution
New average
Runs in 10 innings = 10 × 50 = 500.
New total = 500 + 110 = 610.
Innings = 11.
New average = ≈ 55.45 — option (c).
65
In a quadrilateral PQRS, angles P, Q and R are in the ratio 2 : 3 : 4. If angle S = 90°, what is angle Q?
A.90°
B.72°
C.45°
D.120°
Solution
Angles of a quadrilateral
The four angles of a quadrilateral add up to 360°.
2x + 3x + 4x + 90° = 360° ⇒ 9x = 270°.
x = 30°.
Angle Q = 3x = 90° — option (a).
66
A combo offer says, "Buy 3 shirts at ₹800 each, get a fourth shirt free." What is the effective price per shirt?
A.₹200
B.₹600
C.₹1,100
D.₹400
Solution
Buy 3 get 1 free
The customer pays for 3 shirts: 3 × 800 = ₹2,400.
He takes home 4 shirts.
Effective price = .
= ₹600 — option (b).
67
Two taps can fill a tub in 10 minutes and 15 minutes respectively. A pipe can empty it in 12 minutes. If all three are kept open simultaneously, when will the tub be full?
A.3 min
B.6 min
C.9 min
D.12 min
Solution
Two taps and a leak
Take the tub as LCM(10, 15, 12) = 60 units.
Taps fill 6 and 4 units per minute; the pipe empties 5 units per minute.
Net rate = 6 + 4 − 5 = 5 units per minute.
Time = = 12 minutes — option (d).
68
In a company, the average salary of 3 junior employees is ₹25,000 and that of 2 senior employees is ₹50,000. What is the combined average salary?
A.₹25,000
B.₹48,000
C.₹35,000
D.₹35,500
Solution
Combined average
Juniors total = 3 × 25,000 = ₹75,000.
Seniors total = 2 × 50,000 = ₹1,00,000.
Combined total = ₹1,75,000 over 5 employees.
= ₹35,000 — option (c).
69
A container has an 80-litre mixture of milk and water in the ratio 3 : 1. 12 litres is removed and replaced with water. Then 12 litres is removed again and replaced with milk. What is the final percentage of water?
A.21.25%
B.30.81%
C.25.25%
D.20.25%
Solution
Double replacement
Start: milk 60 L, water 20 L. Removing 12 L takes away = of each.
After the first replacement: milk = 60 − 9 = 51 L, water = 20 − 3 + 12 = 29 L.
Removing 12 L again takes of each: milk = 51 − 7.65 = 43.35, water = 29 − 4.35 = 24.65; then 12 L of milk is added.
Water% = × 100 ≈ 30.81% — option (b).
70
If sinA = and A is acute, find cotA.
A.
B.
C.
D.
Solution
cotA from sinA
Perpendicular = 35 and hypotenuse = 37.
Base = = = = 12.
cotA = .
= — option (b).
If A + B = 90° and sinA = , determine the value of sinA × sinB.
A.
B.
C.
D.
Solution
Complementary angles
B = 90° − A, so sinB = sin(90° − A) = cosA.
With sinA = , the (3, 4, 5) triplet gives cosA = .
sinA × sinB = sinA × cosA = × .
= — option (c).
73
In a right-angled triangle, the point of intersection of the altitudes is found at which of the following points?
A.At the midpoint of the hypotenuse
B.At the vertex where the right angle is formed
C.Somewhere on the hypotenuse, but not exactly in the middle
D.At the midpoint of any side
Solution
Orthocentre
In a right triangle the two legs are themselves altitudes, since they are perpendicular to each other.
They meet at the right-angled vertex, and the third altitude also passes through it.
So the orthocentre sits at that vertex.
Hence option (b).
74
A circle has a radius of 29 cm. A chord is drawn at a distance of 20 cm from the centre. What is the length of the chord?
A.34 cm
B.42 cm
C.28 cm
D.24 cm
Solution
Chord length
The perpendicular from the centre bisects the chord, giving a right triangle.
Half-chord = = .
= = 21 cm.
Chord = 2 × 21 = 42 cm — option (b).
75
A tangent is drawn from a point 20 cm from the centre of a circle of radius 12 cm. Find the length of the tangent.
A.20 cm
B.17 cm
C.11 cm
D.16 cm
Solution
Tangent length
The radius meets the tangent at right angles, so we get a right triangle.
Tangent = .
= = .
= 16 cm — option (d).
Finished reading? Now test yourself.
The same 25 questions, but with a timer and the answers hidden — 15 minutes.
Write 11 as 8 + 3 and 4 as 2.
So 11 + 4 = ( + )².
Taking the square root gives + .
= 2 + — option (b).
Overall rate = × 100 = 5.2%.
By alligation: (6 − 5.2) : (5.2 − 4) = 0.8 : 1.2 = 2 : 3.
So the 4% part is of the total.
× 10,000 = ₹4,000 — option (d).
Take the total distance as D; each part is .
Total time = + + = = .
Average speed = = .
= 18 km/h — option (c).
Let the height be h. At 45° the distance from the foot equals h.
At 30° the distance is h + 20, and tan30° = = .
h = h + 20 ⇒ h( − 1) = 20 ⇒ h = .
Rationalising: h = 10( + 1) m — option (a).
Tank volume = 15 × 14 × 9 = 1890 cm³.
The largest ball is limited by the SMALLEST dimension, 9 cm, so its radius is 4.5 cm.
Ball volume = π(4.5)³ = 121.5π cm³.
Empty space = (1890 − 121.5π) cm³ — option (d).
P’s 9 parts equal ₹27,000.
So 1 part = = ₹3,000.
Q has 7 parts = 7 × 3,000.
= ₹21,000 — option (c).
Each interior angle = .
Pentagon: = 108°.
Decagon: = 144°.
Ratio = 108 : 144 = 3 : 4 — option (a).
Let the numbers be 8x and 9x.
= ⇒ 19(8x + 8) = 17(9x + 8).
152x + 152 = 153x + 136 ⇒ x = 16.
The numbers are 128 and 144 — option (b).
= × × .
= × × .
= .
= 8 : 7 — option (a).
Green share = 100% − 25% − 40% = 35%.
35% of the total = 70.
Total = .
= 200 — option (c).
Questions answered = 180 × = 144.
Correct among them = 144 × = 108.
Unanswered = 180 − 144 = 36, and grace on 25% of these = 9.
Total = 108 + 9 = 117 — option (b).
= .
= = .
Excess of MP over CP = × 100.
= ≈ 53.34% — option (d).
Runs in 10 innings = 10 × 50 = 500.
New total = 500 + 110 = 610.
Innings = 11.
New average = ≈ 55.45 — option (c).
The four angles of a quadrilateral add up to 360°.
2x + 3x + 4x + 90° = 360° ⇒ 9x = 270°.
x = 30°.
Angle Q = 3x = 90° — option (a).
The customer pays for 3 shirts: 3 × 800 = ₹2,400.
He takes home 4 shirts.
Effective price = .
= ₹600 — option (b).
Take the tub as LCM(10, 15, 12) = 60 units.
Taps fill 6 and 4 units per minute; the pipe empties 5 units per minute.
Net rate = 6 + 4 − 5 = 5 units per minute.
Time = = 12 minutes — option (d).
Juniors total = 3 × 25,000 = ₹75,000.
Seniors total = 2 × 50,000 = ₹1,00,000.
Combined total = ₹1,75,000 over 5 employees.
= ₹35,000 — option (c).
Start: milk 60 L, water 20 L. Removing 12 L takes away = of each.
After the first replacement: milk = 60 − 9 = 51 L, water = 20 − 3 + 12 = 29 L.
Removing 12 L again takes of each: milk = 51 − 7.65 = 43.35, water = 29 − 4.35 = 24.65; then 12 L of milk is added.
Water% = × 100 ≈ 30.81% — option (b).
Perpendicular = 35 and hypotenuse = 37.
Base = = = = 12.
cotA = .
= — option (b).
In a right triangle the two legs are themselves altitudes, since they are perpendicular to each other.
They meet at the right-angled vertex, and the third altitude also passes through it.
So the orthocentre sits at that vertex.
Hence option (b).
The perpendicular from the centre bisects the chord, giving a right triangle.
Half-chord = = .
= = 21 cm.
Chord = 2 × 21 = 42 cm — option (b).
The radius meets the tangent at right angles, so we get a right triangle.
Tangent = .
= = .
= 16 cm — option (d).