SSC CGL 13 September 2025 · Shift 1 · Quantitative Aptitude — questions with answers · ShikshaSphere
Chapter 15 of 192
13 September 2025 · Shift 1
Quantitative Aptitude
25 questions ~25 min readFree
25 questions
A
51
Suppose x = + , y = + 1, and z = 3 + 1; then which of the following is true?
A.x < y < z
B.z < y < x
C.y < x < z
D.x < z < y
Solution
Surds — ordering
x = + ≈ 1.414 + 1.732 = 3.146.
y = + 1 ≈ 2.449 + 1 = 3.449; z = 3 + 1 ≈ 4.243 + 1 = 5.243.
So x < y < z — option (a).
52
The budget for a construction project is allocated to land acquisition, building materials, and labor in the ratio 4 : 3 : 3. During the project, the cost of land acquisition rose by 8%, building materials rose by 12%, and labor fell by 15%. What is the percent change (increase or decrease) in the total project cost?
A.1.5% increase
B.2.3% decrease
C.2.3% increase
D.1.5% decrease
Solution
Percentage — weighted change
Take costs 4, 3 and 3 (total 10).
New values: 4 × 1.08 = 4.32; 3 × 1.12 = 3.36; 3 × 0.85 = 2.55 — new total = 10.23.
Change = × 100 = 2.3% increase — option (c).
Pankaj, Kuldeep, and Ankit invested ₹25,000, ₹35,000, and ₹40,000 respectively in a business. If the profit at the end of the year was ₹30,000, find Kuldeep's share.
X and Y started a business by investing ₹48,000 and ₹72,000 respectively. After 6 months, X withdrew half of his capital, while Y increased his capital by ₹24,000. At the end of the year, they earned a total profit of ₹55,000. What is Y's share in the profit?
Study the following table showing the daily wages (in ₹) of 5 workers over 4 days.
Day
A
B
C
D
E
Monday
200
180
220
160
190
Tuesday
210
175
230
170
195
Wednesday
190
185
215
180
200
Thursday
220
190
225
175
205
What is the average daily earning of Worker C?
A.222.5
B.220
C.232.5
D.230.5
Solution
Table — average wages
Worker C's wages: 220, 230, 215, 225.
Total = 890 over 4 days.
Average = = 222.5 — option (a).
57
In a city, the current number of literate people is 25,000. If the number of literate females decreases by 5% and the number of literate males increases by 10%, the total literate population becomes 25,250. What is the present number of literate females in the city?
A.17,500
B.13,000
C.15,000
D.18,000
Solution
Percentage — literate population
Let females = F; then males = 25000 − F.
0.95F + 1.1(25000 − F) = 25250 ⇒ 27500 − 0.15F = 25250.
0.15F = 2250 ⇒ F = 15,000 — option (c).
58
A baker ordered 10 kg of premium flour and some additional kg of standard flour. The price of premium flour per kg was twice that of the standard flour. Due to an ordering error, the quantities of the two types of flour were interchanged. This decreased the total cost by 20%. Find the ratio of the quantity of premium flour to standard flour in the original order.
A.2 : 1
B.5 : 2
C.3 : 4
D.4 : 5
Solution
Ratio — interchanged flour
Let standard price = p (premium = 2p) and standard quantity = S. Original cost = 10(2p) + Sp = (20 + S)p.
After interchange: cost = S(2p) + 10p = (2S + 10)p = 0.8(20 + S)p.
2S + 10 = 16 + 0.8S ⇒ 1.2S = 6 ⇒ S = 5 ⇒ ratio = 10 : 5 = 2 : 1 — option (a).
59
A shopkeeper sold 15 lunch boxes for ₹3000 and gained a profit of 25%. How many lunch boxes should he sell for ₹2816 to make a profit of 10%?
A.14
B.16
C.20
D.19
Solution
Profit — lunch boxes
SP per box = = ₹200 at 25% profit ⇒ CP per box = = ₹160.
For 10% profit, SP per box = 160 × 1.1 = ₹176.
Boxes = = 16 — option (b).
60
A trader sells one brand of coffee at ₹150 per kg, incurring a 25% loss. He also sells another brand of coffee at ₹200 per kg, incurring a 20% loss. If he mixes the two brands in equal proportions and sells the mixture at ₹175 per kg, what is his overall profit or loss percentage?
A.Loss of 22.22%
B.Profit of 20.20%
C.Loss of 20.20%
D.Profit of 22.22%
Solution
Mixture — coffee loss
CP of brand 1 = = ₹200; CP of brand 2 = = ₹250.
Equal mix: CP per kg = = ₹225; SP = ₹175 — loss of ₹50 per kg.
Loss% = × 100 = 22.22% — option (a).
61
Manoj and Rahul together can complete a work in 12 days. Rahul and Sandeep together can complete the same work in 15 days. Sandeep and Manoj together can do it in 20 days. In how many days can Manoj alone complete the job?
A.30 days
B.25 days
C.40 days
D.35 days
Solution
Work — pairs
Daily rates: M + R = , R + S = , S + M = .
Adding: 2(M + R + S) = + + = = ⇒ M + R + S = .
M = − = ⇒ Manoj alone takes 30 days — option (a).
62
From a 64-liter container of pure milk, 8 liters are removed and replaced by water. This operation is performed a total of three times. What is the final quantity of milk remaining in the container?
A.44.44 liters
B.55.45 liters
C.40.42 liters
D.42.88 liters
Solution
Repeated replacement
Each operation leaves = of the milk.
After three operations: 64 × = 64 × .
= 42.875 ≈ 42.88 litres — option (d).
63
A juice vendor mixes water with pure mango juice. If he sells the mixture at the cost price of pure mango juice and makes a profit of 20%, what is the ratio of water to pure mango juice in the mixture, respectively?
A.3 : 2
B.1 : 5
C.2 : 3
D.5 : 1
Solution
Water in juice — profit
Selling at the CP of pure juice with 20% profit means every 5 parts of juice are billed as 6.
The extra 1 part is free water on 5 parts of juice.
Water : Juice = 1 : 5 — option (b).
64
A car covers 50% of a certain distance at a pace of 40 km/h and the remaining distance at a pace of 60 km/h. What is the average speed of the car for the entire journey?
A.46 km/h
B.48 km/h
C.26 km/h
D.24 km/h
Solution
Average speed — equal distances
For equal distances, average speed = .
= = .
= 48 km/h — option (b).
65
Aditya and Harish are jogging around a park's circular track which has a perimeter of 1.2 km. They start from the same point at 6:00 a.m. and run in opposite directions. Aditya's speed is 5 km/h, and Harish's speed is 7 km/h. At what time will they meet for the fifth time?
A.6:00 AM
B.6:30 AM
C.6:40 AM
D.7:15 AM
Solution
Circular track — 5th meeting
Running in opposite directions, relative speed = 5 + 7 = 12 km/h.
They meet every hour = 6 minutes.
Fifth meeting after 5 × 6 = 30 minutes — at 6:30 AM; option (b).
66
The area of a sector of a circle with radius 21 cm and central angle 180° is:
What is the area of a sector with a central angle of 60° and radius 4 cm?
A. cm²
B. cm²
C. cm²
D. cm²
Solution
Sector area — 60°
Sector area = × r² = × × 16.
= .
= cm² — option (a).
69
Which of these lines is parallel to 4x − 5y = 10?
A.5x − 4y = 10
B.4x + 5y = 15
C.4x − 5y = 15
D.x + y = 10
Solution
Parallel lines
Parallel lines have equal slopes — the coefficients of x and y must be in the same ratio.
4x − 5y = 15 has exactly the same coefficients (slope ) with a different constant.
Hence option (c).
70
If cos(90° − x) = sin(2x), then what is x?
A.0°
B.30°
C.25°
D.15°
Solution
Trigonometric equation
cos(90° − x) = sin x, so the equation becomes sin x = sin 2x.
sin 2x − sin x = 0 ⇒ sin x (2cos x − 1) = 0 ⇒ x = 0° (or cos x = ).
Among the options, x = 0° satisfies it — option (a).
In triangles ABC and PQR, if the lengths of the sides are such that AB equals PQ, BC equals QR, and CA equals RP, which congruence rule demonstrates that triangle ABC is congruent to triangle PQR?
A.SSS
B.SAS
C.ASA
D.AAS
Solution
Congruence — SSS
All three pairs of corresponding sides are equal.
This is exactly the Side-Side-Side condition.
Hence SSS — option (a).
73
Given, A and B are complementary angles, and cos A = , what is tan B?
A.
B.
C.
D.
Solution
Complementary angles
A + B = 90°, so tan B = tan(90° − A) = cot A.
cos A = ⇒ sin A = ⇒ cot A = .
Hence tan B = — option (a).
74
In a cyclic quadrilateral PQRS, if angle P is 110°, what is the measure of angle R?
A.60°
B.70°
C.90°
D.120°
Solution
Cyclic quadrilateral
In a cyclic quadrilateral, opposite angles are supplementary.
P + R = 180° ⇒ R = 180° − 110°.
= 70° — option (b).
x = + ≈ 1.414 + 1.732 = 3.146.
y = + 1 ≈ 2.449 + 1 = 3.449; z = 3 + 1 ≈ 4.243 + 1 = 5.243.
So x < y < z — option (a).
Investment ratio = 25000 : 35000 : 40000 = 5 : 7 : 8 (total 20 parts).
Kuldeep's share = × 30000.
= ₹10,500 — option (d).
X: 48000 × 6 + 24000 × 6 = 2,88,000 + 1,44,000 = 4,32,000 capital-months.
Y: 72000 × 6 + 96000 × 6 = 4,32,000 + 5,76,000 = 10,08,000 — ratio X : Y = 3 : 7.
Y's share = × 55000 = ₹38,500 — option (c).
SP per box = = ₹200 at 25% profit ⇒ CP per box = = ₹160.
For 10% profit, SP per box = 160 × 1.1 = ₹176.
Boxes = = 16 — option (b).
CP of brand 1 = = ₹200; CP of brand 2 = = ₹250.
Equal mix: CP per kg = = ₹225; SP = ₹175 — loss of ₹50 per kg.
Loss% = × 100 = 22.22% — option (a).
Daily rates: M + R = , R + S = , S + M = .
Adding: 2(M + R + S) = + + = = ⇒ M + R + S = .
M = − = ⇒ Manoj alone takes 30 days — option (a).
Each operation leaves = of the milk.
After three operations: 64 × = 64 × .
= 42.875 ≈ 42.88 litres — option (d).
Selling at the CP of pure juice with 20% profit means every 5 parts of juice are billed as 6.
The extra 1 part is free water on 5 parts of juice.
Water : Juice = 1 : 5 — option (b).
For equal distances, average speed = .
= = .
= 48 km/h — option (b).
Running in opposite directions, relative speed = 5 + 7 = 12 km/h.
They meet every hour = 6 minutes.
Fifth meeting after 5 × 6 = 30 minutes — at 6:30 AM; option (b).
Sector area = × r² = × × 21 × 21.
= × 1386.
= 693 cm² — option (a).
Sector area = × r² = × × 16.
= .
= cm² — option (a).
Parallel lines have equal slopes — the coefficients of x and y must be in the same ratio.
4x − 5y = 15 has exactly the same coefficients (slope ) with a different constant.
Hence option (c).
All three pairs of corresponding sides are equal.
This is exactly the Side-Side-Side condition.
Hence SSS — option (a).
A + B = 90°, so tan B = tan(90° − A) = cot A.
cos A = ⇒ sin A = ⇒ cot A = .
Hence tan B = — option (a).
In a cyclic quadrilateral, opposite angles are supplementary.
P + R = 180° ⇒ R = 180° − 110°.
= 70° — option (b).