SSC CGL Mock – Tier I Mock Test 06 – Section C · Quantitative Aptitude

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SSC CGL Mock – Tier I Mock Test 06 – 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.  
A 240 m long train overtakes a man walking at 6 km/h in the same direction in 16 seconds. What is the speed of the train?

Correct Answer: C [60 km/h]

Explanation:

Relative speed = 240/16 = 15 m/s = 54 km/h → train = 54 + 6 = 60 km/h.

2.  
On ₹ 25,000 for 2 years at 8% a year, by how much does compound interest (compounded yearly) exceed simple interest?

Correct Answer: B [₹ 160]

Explanation:

Difference = P(r/100)² = 25,000 × 0.0064 = 160.

3.  
From a can holding 90 litres of pure milk, 9 litres are removed and replaced by water. The same is done a second time. How many litres of milk does the can now hold?

Correct Answer: D [72.9 litres]

Explanation:

90 × (1 − 9/90)² = 90 × 0.81 = 72.9 litres.

4.  
A wheel of radius 35 cm rolls without slipping. How many complete turns does it make in covering 1.1 km? (Take π = 22/7)

Correct Answer: A [500]

Explanation:

Circumference = 2 × 22/7 × 35 = 220 cm; 1,10,000 ÷ 220 = 500.

5.  
A solid hemisphere has radius 21 cm. Find the area of its whole surface, curved and flat together. (Take π = 22/7)

Correct Answer: D [4,158 cm²]

Explanation:

3πr² = 3 × 22/7 × 441 = 4,158 cm².

6.  
For every angle θ, (sin θ + cos θ)² + (sin θ − cos θ)² is equal to:

Correct Answer: C [2]

Explanation:

Expanding, the cross terms cancel: 2(sin² θ + cos² θ) = 2.

7.  
θ is acute and satisfies 4 sin² θ = 3. Evaluate tan θ + cot θ.

Correct Answer: B [4√3/3]

Explanation:

sin θ = √3/2 → θ = 60° → √3 + 1/√3 = 4/√3 = 4√3/3.

8.  
The average mark of 40 students was found to be 62. Later it was found that a mark of 84 had been copied as 48. What is the correct average?

Correct Answer: B [62.9]

Explanation:

The total rises by 84 − 48 = 36 → average rises by 36/40 = 0.9 → 62.9.

9.  
A alone takes 24 days for a job and B alone 36 days. They begin together, but A quits after 8 days. How many more days does B need to finish?

Correct Answer: C [16 days]

Explanation:

In 8 days they do 8 × 5/72 = 5/9; B does the remaining 4/9 in 16 days.

10.  
Diagram-basedO is the circumcentre of triangle ABC (see figure) and ∠BAC = 64°. Find ∠BOC.

Correct Answer: D [128°]

Explanation:

The angle at the centre is twice the angle at the circumference on the same arc: 2 × 64° = 128°.

11.  
In an acute triangle ABC, the altitudes from B and C meet at H. If ∠A = 50°, find ∠BHC.

Correct Answer: A [130°]

Explanation:

Answer: 130°. ∠BHC = 180° − ∠A = 130°.

12.  
Diagram-basedIn the figure, PT is a tangent and PAB is a secant of the circle. If PT = 12 cm and PA = 8 cm, find AB.

Correct Answer: A [10 cm]

Explanation:

PT² = PA × PB → PB = 144/8 = 18 → AB = 18 − 8 = 10 cm.

13.  
Two numbers are in the proportion 5 : 7. Reducing each by 6 changes the proportion to 3 : 5. Find the larger of the original numbers.

Correct Answer: D [21]

Explanation:

(5x − 6)/(7x − 6) = 3/5 → 25x − 30 = 21x − 18 → x = 3 → larger = 21.

14.  
Ajay sells two phones at ₹ 9,900 apiece, gaining 10% on one and losing 10% on the other. Taking both deals together, what is his position?

Correct Answer: C [1% loss]

Explanation:

Costs 9,000 and 11,000 = 20,000; sales 19,800 → loss of 1%.

15.  
A shopkeeper marks his goods 30% above cost and then allows a discount of 12%. What is his profit per cent?

Correct Answer: B [14.4%]

Explanation:

1.30 × 0.88 = 1.144 → profit 14.4%.

16.  
The population of a village is 15,625. It falls by 4% every year. What will the population be after 3 years?

Correct Answer: D [13,824]

Explanation:

Answer: 13,824. 15,625 × (24/25)³ = 13,824.

17.  
How many numbers between 200 and 600 are divisible by each of 4, 6 and 9?

Correct Answer: A [11]

Explanation:

LCM(4, 6, 9) = 36; multiples of 36 from 216 to 576 → 16 − 6 + 1 = 11.

18.  
Find the largest number which divides 1,118, 1,544 and 2,182 so that the remainders are 5, 7 and 9 in that order.

Correct Answer: B [53]

Explanation:

HCF of 1,113, 1,537 and 2,173 = 53 (1,113 = 53 × 21, 1,537 = 53 × 29, 2,173 = 53 × 41).

19.  

Directions (Q 69–72): The bar chart shows the exports and imports (in ₹ crore) of a company in five years (fictional data).

Bar chartFor how many of the years shown were exports greater than imports?

Correct Answer: C [4]

Explanation:

2021, 2022, 2024 and 2025 → 4 years.

20.  
(Use the directions above – Q 69–72)
Bar chartAdd up the company's imports for all five years. What is the total?

Correct Answer: B [₹ 670 crore]

Explanation:

100 + 125 + 150 + 140 + 155 = 670.

21.  
(Use the directions above – Q 69–72)
Bar chartIn which year were exports largest relative to imports (highest exports ÷ imports)?

Correct Answer: D [2021]

Explanation:

Ratios: 1.2, 1.12, 0.9, 1.14, 1.16 → 2021.

22.  
(Use the directions above – Q 69–72)
Bar chartExports in 2025 were higher than exports in 2023 by what per cent?

Correct Answer: C [33 1/3%]

Explanation:

(180 − 135)/135 × 100 = 33 1/3%.

23.  
For a non-zero number x with x + x⁻¹ = 3, the value of x³ + x⁻³ is:

Correct Answer: A [18]

Explanation:

x³ + x⁻³ = (x + x⁻¹)³ − 3(x + x⁻¹) = 27 − 9 = 18.

24.  
Solve the pair 5x − 3y = 11 and 2x + y = 11, and find x² + y².

Correct Answer: C [25]

Explanation:

From the second, y = 11 − 2x; 5x − 33 + 6x = 11 → x = 4, y = 3 → 25.

25.  
If p + q = 8 and p³ + q³ = 152, what is pq?

Correct Answer: D [15]

Explanation:

p³ + q³ = (p + q)³ − 3pq(p + q) → 152 = 512 − 24pq → pq = 15.

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