SSC CGL Mock – Tier I Mock Test 03 – Section C · Quantitative Aptitude

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SSC CGL Mock – Tier I Mock Test 03 – 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.  
In a class of 24 students the average age is 13 years. Adding the class teacher to the group raises the average by one year. Find the teacher's age.

Correct Answer: B [38 years]

Explanation:

25 × 14 − 24 × 13 = 350 − 312 = 38 years.

2.  
15 workers can build a wall in 20 days. In how many days can 25 workers build the same wall?

Correct Answer: A [12 days]

Explanation:

15 × 20 = 300 worker-days → 300/25 = 12 days.

3.  
Sunita cycles from her village to the market at 24 km/h and comes back along the same road at 40 km/h. Find her average speed for the round trip.

Correct Answer: C [30 km/h]

Explanation:

2 × 24 × 40/(24 + 40) = 30 km/h.

4.  
Find the area of a triangle whose sides are 11 cm, 13 cm and 20 cm.

Correct Answer: B [66 cm²]

Explanation:

s = 22 → √(22 × 11 × 9 × 2) = √4356 = 66 cm².

5.  
A cylindrical pillar of radius 7 cm and height 10 cm is to be wrapped with paper round its side only. What area of paper is needed? (Take π = 22/7)

Correct Answer: C [440 cm²]

Explanation:

2πrh = 2 × 22/7 × 7 × 10 = 440 cm².

6.  
When x and y are in the ratio 3 : 4, what is the ratio of (5x − 2y) to (3x + y)?

Correct Answer: A [7 : 13]

Explanation:

Put x = 3, y = 4: (15 − 8) : (9 + 4) = 7 : 13.

7.  
Using the identity (a + b)(a − b) = a² − b², the value of 103 × 97 is:

Correct Answer: D [9,991]

Explanation:

(100 + 3)(100 − 3) = 10,000 − 9 = 9,991.

8.  
At which point do the lines 2x + y = 8 and x − y = 1 intersect?

Correct Answer: D [(3, 2)]

Explanation:

Adding: 3x = 9 → x = 3, then y = 2 → (3, 2).

9.  
Neha lent ₹ 6,000 at simple interest and received ₹ 15,000 in all at the end of 15 years. What was the rate of interest per annum?

Correct Answer: A [10%]

Explanation:

Interest = 15,000 − 6,000 = 9,000 → rate = 9,000 × 100/(6,000 × 15) = 10%.

10.  
What is the measure, in radians, of each interior angle of a regular pentagon?

Correct Answer: B [3π/5]

Explanation:

Interior angle = 108° = 108 × π/180 = 3π/5.

11.  
From a point on level ground, the angle of elevation of the top of a tower 50√3 m high is 60°. How far is the point from the foot of the tower?

Correct Answer: C [50 m]

Explanation:

Answer: 50 m. tan 60° = 50√3/d → d = 50 m.

12.  
The ratio of a to b is 2 : 5 and the ratio of b to c is 3 : 4. Combine them into one ratio a : b : c.

Correct Answer: A [6 : 15 : 20]

Explanation:

Make b equal: 2 : 5 = 6 : 15 and 3 : 4 = 15 : 20 → 6 : 15 : 20.

13.  
A number is first increased by 30% and the result is then decreased by 30%. What is the net effect on the number?

Correct Answer: D [9% decrease]

Explanation:

1.3 × 0.7 = 0.91 → a net decrease of 9%.

14.  
Counting 1 and the number itself, how many whole numbers divide 360 exactly?

Correct Answer: B [24]

Explanation:

360 = 2³ × 3² × 5 → (3 + 1)(2 + 1)(1 + 1) = 24.

15.  
The recurring decimal 0.27 (only the 7 repeats) is equal to:

Correct Answer: C [5/18]

Explanation:

0.2 7 = (27 − 2)/90 = 25/90 = 5/18.

16.  
By selling a cycle for ₹ 2,700 a shopkeeper loses 10%. What did the cycle cost him?

Correct Answer: C [₹ 3,000]

Explanation:

Answer: ₹ 3,000. 2,700 ÷ 0.9 = 3,000.

17.  
Goods are marked 40% above cost price and sold at a discount of 25%. What is the result?

Correct Answer: B [5% profit]

Explanation:

1.4 × 0.75 = 1.05 → profit of 5%.

18.  
A 30-litre mixture of milk and water contains 20% water. How much water must be added so that water becomes 40% of the mixture?

Correct Answer: A [10 litres]

Explanation:

Milk 24 L must be 60% of the new mixture → total 40 L → add 10 L of water.

19.  
Diagram-basedIn the figure, lines l and m are parallel and are cut by a transversal. Find x.

Correct Answer: D [115°]

Explanation:

x and 65° are interior angles on the same side of the transversal → x = 180° − 65° = 115°.

20.  
In triangle ABC, D lies on AB and E on AC with DE ∥ BC. If AD = 4 cm, DB = 6 cm and BC = 15 cm, what is DE?

Correct Answer: B [6 cm]

Explanation:

ΔADE ~ ΔABC → DE/BC = AD/AB = 4/10 → DE = 6 cm.

21.  
AC is a diameter of a circle and B is a point on the circle. If ∠BAC = 35°, what is ∠BCA?

Correct Answer: A [55°]

Explanation:

The angle in a semicircle is 90° (∠ABC), so ∠BCA = 90° − 35° = 55°.

22.  

Directions (Q 72–75): The pie chart shows how a school's annual expenditure of ₹ 40 lakh is divided among six heads (fictional data).

Pie chartHow many degrees does the Laboratory slice of the pie chart occupy at the centre?

Correct Answer: D [43.2°]

Explanation:

Answer: 43.2°. 12% of 360° = 43.2°.

23.  
(Use the directions above – Q 72–75)
Pie chartHow much does the school spend on Salaries?

Correct Answer: C [₹ 18 lakh]

Explanation:

Answer: ₹ 18 lakh. 45% of ₹ 40 lakh = ₹ 18 lakh.

24.  
(Use the directions above – Q 72–75)
Pie chartBy how much does the combined spending on Library and Sports exceed the spending on Maintenance?

Correct Answer: D [₹ 1.2 lakh]

Explanation:

(10 + 8 − 15)% = 3% of ₹ 40 lakh = ₹ 1.2 lakh.

25.  
(Use the directions above – Q 72–75)
Pie chartWhat is the ratio of the spending on Sports to that on Laboratory?

Correct Answer: C [2 : 3]

Explanation:

Answer: 2 : 3. 8 : 12 = 2 : 3.

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