SSC CGL Mock – Tier I Mock Test 15 – Section C · Quantitative Aptitude
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Horizontal distances 1,500 m and 4,500 m → 3,000 m in 15 s = 200 m/s = 720 km/h.
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SSC CGL Mock – Tier I Mock Test 15 – Section C · Quantitative Aptitude – 25 questions, subject: Full Mock Tests. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.
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1.
The compound interest on a sum for the 2nd year is ₹ 1,320 and for the 3rd year is ₹ 1,452 (compounded annually). What is the sum?
Correct Answer: B [₹ 12,000]
Explanation:
Rate = 132/1,320 = 10%; 2nd-year interest = P × 1.1 × 0.1 = 0.11P = 1,320 → P = 12,000.
2.
The salaries of A, B and C are in the ratio 2 : 3 : 5. If they get increments of 15%, 10% and 20% respectively, what is the new ratio of their salaries?
Correct Answer: A [23 : 33 : 60]
Explanation:
2 × 1.15 : 3 × 1.10 : 5 × 1.20 = 2.3 : 3.3 : 6 = 23 : 33 : 60.
3.
Mr Iyer buys a flat for ₹ 45 lakh and spends 10% of that on repairs. He later sells it at a loss of 4% on his total cost. What is the selling price?
Correct Answer: C [₹ 47.52 lakh]
Explanation:
Total cost = 49.5 lakh; 96% of it = 47.52 lakh.
4.
A trader marks his goods so that even after two successive discounts of 10% each he makes a profit of 21.5%. By what per cent above cost does he mark them?
Correct Answer: A [50%]
Explanation:
Marked = 1.215 ÷ 0.81 = 1.5 of cost → 50% above cost.
5.
What is the largest power of 6 that divides 40! exactly?
Correct Answer: D [18]
Explanation:
Power of 3 in 40! = 13 + 4 + 1 = 18; power of 2 = 38; the smaller decides → 6 18 .
6.
Each number from 1 to 10 is raised to its own power and the results are added (1¹ + 2² + … + 10¹⁰). What is the last digit of the total?
Correct Answer: B [7]
Explanation:
Unit digits: 1, 4, 7, 6, 5, 6, 3, 6, 9, 0 → sum 47 → unit digit 7.
7.
What is the ratio of the area of the circumcircle of a square to the area of its incircle?
Correct Answer: B [2 : 1]
Explanation:
R = a/√2 and r = a/2 → R² : r² = 1/2 : 1/4 = 2 : 1.
8.
A sphere just fits inside a cubical box of edge 12 cm. What volume of the box is left empty?
Correct Answer: A [(1728 − 288π) cm³]
Explanation:
Sphere radius 6 → (4/3)π × 216 = 288π; empty = 1,728 − 288π cm³.
9.
A does one-third of a job in 5 days and B does two-fifths of it in 8 days. Working together, in how many days can they do the whole job?
Correct Answer: D [8 4/7 days]
Explanation:
A's rate 1/15, B's rate 1/20 → together 7/60 → 8 4/7 days.
10.
y is 25% less than z, and x exceeds y by 20%. By what per cent does z exceed x?
Correct Answer: C [11 1/9%]
Explanation:
x = 1.2 × 0.75z = 0.9z → z is 0.1/0.9 = 11 1/9% more than x.
11.
If a² + ab + b² = 24 and a⁴ + a²b² + b⁴ = 288, what is a² + b²?
Correct Answer: C [18]
Explanation:
a⁴ + a²b² + b⁴ = (a² + ab + b²)(a² − ab + b²) → a² − ab + b² = 12; adding, 2(a² + b²) = 36 → 18.
12.
x, y and z are non-zero numbers with x + y + z = 0. What is the value of (x² + y² + z²)/(xy + yz + zx)?
Correct Answer: D [−2]
Explanation:
0 = (x + y + z)² = x² + y² + z² + 2(xy + yz + zx) → ratio = −2.
13.
The lines x = 2, y = 3 and 3x + 4y = 30 enclose a triangle. What is its area?
Correct Answer: A [6 sq units]
Explanation:
Vertices (2, 3), (2, 6) and (6, 3) → right triangle with legs 3 and 4 → area 6 sq units.
14.
Three kinds of rice costing ₹ 30, ₹ 36 and ₹ 45 per kg are mixed in the ratio 3 : 2 : 1. If the mixture is sold at ₹ 41.40 per kg, what is the profit per cent?
Correct Answer: B [20%]
Explanation:
Cost of mixture = (90 + 72 + 45)/6 = ₹ 34.5 → 41.40/34.5 = 1.2 → 20% profit.
15.
A and B start together from the same point of a 600 m circular track and run in the same direction at 5 m/s and 7 m/s. After how much time will they first meet again at the starting point?
Correct Answer: C [10 minutes]
Explanation:
A is at the start every 120 s and B every 600/7 s; both are there when 5t and 7t are multiples of 600 → t = 600 s.
16.
At the time of their marriage the average age of a couple was 26 years. Seven years later, the average age of the couple and their child is 24 years. How old is the child?
Correct Answer: A [6 years]
Explanation:
Couple now: 2 × 33 = 66; family total 3 × 24 = 72 → child = 6 years.
17.
Diagram-basedIn the figure, AB = AC and ∠ABC = 70°. BD bisects ∠ABC and meets AC at D. Find ∠ADB.
Correct Answer: B [105°]
Explanation:
∠A = 180° − 140° = 40° and ∠ABD = 35° → ∠ADB = 180° − 40° − 35° = 105°.
18.
Two circles of radii 8 cm and 2 cm touch each other externally and both touch a straight line. A third circle touches both circles and the same line. What is its radius?
Correct Answer: D [8/9 cm]
Explanation:
1/√r = 1/√8 + 1/√2 = 3/(2√2) → r = 8/9 cm.
19.
In trapezium ABCD, AB ∥ DC and AB = 2 DC. The diagonals meet at O. If the area of ΔAOB is 84 cm², what is the area of ΔCOD?
Correct Answer: A [21 cm²]
Explanation:
ΔAOB ~ ΔCOD with ratio 2 : 1 → areas 4 : 1 → 84/4 = 21 cm².
20.
Mixed DIWhat was the total amount actually spent?
Directions (Q 70–73): A ₹ 250 crore project budget was allocated among five heads as shown in the pie chart. The table shows the actual spending under each head as a percentage of its allocation (fictional data).
| Head | Land | Construction | Machinery | Labour | Others |
|---|---|---|---|---|---|
| Spent (% of allocation) | 100 | 90 | 80 | 125 | 50 |
Correct Answer: B [₹ 228 crore]
Explanation:
45 + 76.5 + 44 + 50 + 12.5 = 228.
21.
(Use the directions above – Q 70–73)
Mixed DIUnder which head did the actual spending exceed the allocation?
Mixed DIUnder which head did the actual spending exceed the allocation?
Correct Answer: C [Labour]
Explanation:
Only Labour (125% of its allocation).
22.
(Use the directions above – Q 70–73)
Mixed DIBy how much did the spending on Construction exceed the spending on Machinery?
Mixed DIBy how much did the spending on Construction exceed the spending on Machinery?
Correct Answer: D [₹ 32.5 crore]
Explanation:
Answer: ₹ 32.5 crore. 76.5 − 44 = 32.5.
23.
(Use the directions above – Q 70–73)
Mixed DIThe total spending was what percentage of the total budget?
Mixed DIThe total spending was what percentage of the total budget?
Correct Answer: C [91.2%]
Explanation:
Answer: 91.2%. 228/250 × 100 = 91.2%.
24.
Find the value of (sin 35° cos 55° + cos 35° sin 55°) ÷ (cosec² 10° − tan² 80°).
Correct Answer: A [1]
Explanation:
Numerator = sin 90° = 1; tan 80° = cot 10° so the denominator = cosec² 10° − cot² 10° = 1 → 1.
25.
From a point on the ground, the angle of elevation of an aircraft flying horizontally at a height of 1500√3 m is 60°. After 15 seconds the angle becomes 30°. What is the speed of the aircraft?
Correct Answer: B [720 km/h]
Explanation:
Horizontal distances 1,500 m and 4,500 m → 3,000 m in 15 s = 200 m/s = 720 km/h.
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