This is the sample paper for the SSC CGL pre-examination of the Aptitude section. It comprises 25 questions as per the latest SSC CGL pattern with shortcut solutions. 25 questions are asked in each section of the SSC CGL pre-examination. Aspirants usually face problems in solving the Quant section with the right speed & accuracy and hence lose on some sure shot marks. This sample paper will make you ready for the real exam by improving your speed & accuracy.
Que 1. Two numbers are in the ratio of 5: 12. If 3 is added to the first number and 4 is added to the second number, then the ratio becomes 1: 2. What are the original numbers?
A) 5 and 12
B) 10 and 24
C) 15 and 36
D) 20 and 48
Answer: A
Explanation:
Let the given numbers be 5x and 12x
A.T.Q
(5x + 3)/(12x + 4) = 1/2
10x + 6 = 12x + 4
2x = 2
x = 1
Here the correct answer is option A
Que 2. The average of 11 numbers is 19.4. If the 12th number is added then the average of 12 numbers be 22.6. What is the 12th number?
A)52.6
B)48.6
C)57.8
D)56.4
Answer: C
Explanation:
Let the 12th number be x
The average of 11 numbers is 19.4
Then the total of 11 numbers = 19.4 × 11 = 213.4
Now, the average of 12 numbers = 22.6
Then the total of 12 numbers = 12 × 22.6 =271.2
12th number = Total of 12 numbers – Total of 11 numbers
= 271.2 – 213.4
= 57.8
Here the correct answer is option C
Que 3. If 38x47y is divisible by 72, then find 2x+3y?
A)8
B)10
C)12
D)14
Answer: C
Explanation:
For a number to be divisible by 72 a number must be divisible by 9 and 8.
For a number to be divisible by 8, the last 3 digits of a number must be divisible by 8.
Then the only possible value of y is 2.
Now, for a number to be divisible by 9 then the sum of the digits of a given number must be divisible by 9.
Then, the only possible value of x is 3.
Now, 2x+3y = 2 × 3 + 3 × 2
= 6 + 6
= 12.
Here the correct answer is option C
Que 4. P can complete half of the work in 12 days and Q can complete one- third the work in 10 days. If P started and works for 6 days then Q joined. How many days did they take in total to complete the work?
A)12
B)14
C)16
D)18
Answer: C
Explanation:
P can complete half the work in 12 days then P can complete the whole work in 24 days
Q can complete 1/3 work in 10 days then Q can complete the whole work in 30 days.
Let the total work be 120 units (LCM of 24 and 30)
Work done by P & Q in 1 day is 5 units & 4 units respectively.
Work done by P in 6 days = Efficiency of P × 6
= 5 × 6
= 30 units.
Remaining work = 120 – 30 units
= 90 units
Time taken by P & Q to complete the remaining work = Remaining work/Efficiency of ( P & Q) = 90/9 =10 days
Total days = 6 + 10 days
= 16 days.
Here the correct answer is option C
Que 5. A person borrows Rs 24000 at a 10% p.a. compounded annually half yearly, then how much more money he has to give as interest after 1 year?
A) 40
B) 60
C) 80
D)100
Answer: B
Explanation:
Amount after 1 year = Principle × (100 + r/100)n
= 24000 × 110/100
= 26400
Interest as yearly = 26400 – 24000
= 2400
If the interest is compounded half yearly then, the rate becomes half, and time becomes double.
Rate = 10/2 = 5% and 1 year = 2 half year.
Amount = Principle × (100 + r/100)n
= 24000 × (105/100) × (105/100)
= 26460
Interest when compounded half yearly = 26460 – 24000 = 2460
Required difference = 2460-2400 = Rs 60.
Here the correct answer is option B
Que 6. If the shopkeeper gains 20% by selling the article at a discount of 30% on the marked price and the marked price of the article is Rs1500. Then find its CP.
A)725
B)775
C)825
D)875
Answer: D
Explanation:
SP of the article = 1500 × 70/100 = 1050.
CP of the article when the article was sold at a profit of 20% = 1050/1.2 = 875.
Here the correct answer is option D
Que 7. If A sells the article at 20% profit to B and B sells it at a 25% profit to C and C sells it to D at a loss of 20 %. D pays Rs 600 then how much does it cost to A?
A)400
B)500
C)600
D)700
Answer: B
Explanation:
A sold the article to B at 20 % Profit, B sold at 25 % profit to C & then C sold it at 20% loss to D ( D pays 600 Rs)
It means, A × (120/100) × (125/100) × (80/100) = 600
Hence cost price of A = Rs 500
Here the correct answer is option B
Que 8. ABCD is a rhombus in which diagonals are 24 cm and 48 cm. Find is the area of the rhombus.
A)476
B)526
C)576
D)672
Answer: C
Explanation:
Area of rhombus = 1/2 × diagonal1 × diagonal2
= 1/2 × 24 × 48 = 576 cm sq
Here the correct answer is option C
Que 9. What is the inradius of a triangle whose sides are 5 cm, 12 cm, and 13 cm?
A)1
B)2
C)3
D)4
Answer: B
Explanation:
(5,12,13) is a Pythagoras triplets.
Hence, it is a right-angled triangle.
Formula to find inradius (r) =(P+B-H)/2
= (5+12-13)/2
= (17-13)/2
= 2 cm.
Here the correct answer is option B
Que 10. The radius of a cone is 8 cm and the height is 15 cm, then find its CSA.
A)154Ï€
B)136Ï€
C)144Ï€
D)172Ï€
Answer: B
Explanation:
Slant height of the cone (l) = √(r2 + h2)
l2 = 225 + 64
I = 17 cm
CSA= πrl
= π × 8 × 17
= 136Ï€.
Here the correct answer is option B
Que 11. A cube of side 12 cm is melted and small cubes of a side of 4 cm are made then how many cubes can be made from it?
A)24
B)27
C)30
D)33
Answer: B
Explanation:
Let the number of cubes that can be made = n
The volume of a big cube = Volume of small a cube × n
12 × 12 × 12 = 4 × 4 × 4 × n
n = 27.
Here the correct answer is option B
Que 12. If 2x + 3y = 15 and 5x – 2y = 10 meets at (a,b). Find (a,b).
A) (60/17,55/17)
B) (60/19,55/19)
C) (55/17,60/17)
D) (55/17,60/19)
Answer: B
Explanation:
Multiply equation 1 by 2 and 2 by 3 & then add both.
We will get x = 60/19, only 1 option satisfies.
Answer: (60/19, 55/19)
Here the correct answer is option B
Que 13. A building is 10 cm high. A person observes it from a point and makes an angle of elevation of 30 degrees. He moves towards the building and makes a 45-degree angle. Find the distance travelled by a person.
A) 10√3
B) 5√3
C) 10√3 – 10
D) 15
Answer: C
Explanation:
In Triangle PQB
Tan 45 =10/QB
1 = 10/QB
QB = 10 cm
Now, in triangle PQA
Tan 30 = 10/QA
1/√3=10/QA
QA= 10√3
AB= 10√3 – 10
Here the correct answer is option C
Que 14. Sin60° × Tan30° × Sin30° × Sec30°
A) 4/3
B) 1/2√3
C) 1/3
D) √3
Answer: B
Explanation:
√3/2 × 1/√3 × 1/2 × 2/√3
=1/2√3
Here the correct answer is option B
Que 15. A is 40% less than B . C is 40% of the sum of A & B . If C is 320. Then find B.
A) 300
B)500
C)800
D)600
Answer: B
Explanation:
Let B be 100 x
Then A = 60x and C = 64x
64x = 320
x = 5
B= 100x
B= 500
Here the correct answer is option B
Que 16. A spends 20% of his salary on food and from the remaining, he spends 10% on clothes and from the rest, he deposited half in the bank account which is Rs 9000. Find his total salary.
A)15000
B)20000
C)25000
D)30000
Answer: C
Explanation:
Let his total salary be x
Then, x × (80/100) × (90/100) × (50/100) = 9000
x = Rs 25000.
Here the correct answer is option C
Que 17. If x+ 1/x = 5 then Find x5+ 1/x5 ?
A)2525
B)2550
C) 2450
D)2475
Answer: A
Explanation:
Given x + 1/x = 5 (Squaring both sides)
We get, x2+1/x2= 25 – 2 = 23 —— Equation 1
x + 1/x = 5 (Take cube on both sides)
We get, x3+1/x3+ 3*15= 125
x3+1/x3=110 ——Equation 2
Multiply equations 1 and 2 we get
x5+x+1/x +1/x5 =23*110 = 2530
x5+1/x5 =2530-5 = 2525
Here the correct answer is option A
Que 18. x2 – 5x + 3 = 0 then Find x2 + 9/x2 = ?
A) 17
B) 19
C) 20
D) 22
Answer: B
Explanation:
On dividing by x, we get
x + 3/x = 5
On squaring both sides we get,
x2 + 9/x2 + 2(x × 3/x) = 25
x2 + 9/x2 = 25 – 6 =19.
Here the correct answer is option B
Que 19. ABC is a triangle of area of 96 cm sq. D is a point on BC such that it divides BC in 2:1, then find the area of triangle ABD.
A)36
B)44
C)64
D)72
Answer: C
Explanation:
The area of the triangle is divided by AD in the ratio of BD: DC ( Ar. ABD: Ar. ADC = BD: DC as the height of both the triangles is the same)
Therefore, area of triangle ABD= (2/3) × 96 = 64 cm sq.
Here the correct answer is option C
Que 20. Raju earns Rs 12000 per month, he spends 1/4 part of his income on food, and 3/10 of the remaining money on house rent. The money saved by Raju is?
A) Rs 4500
B) Rs 6300
C) Rs 5000
D) Rs 1200
Answer: B
Explanation:
Money spent on food = 12000 × 1/4 = 3000
Amount left is 9000.
3/10 of 9000 = 2700.
So the amount he saves is 12000 – 3000 – 2700 = 6300.
Here the correct answer is option B
Que 21. A train starts from Delhi to Jaipur at a speed of 54 km/hr and another train B starts from Jaipur to Delhi at a speed of 36km/hr. The distance between Delhi & Jaipur is 450 Km then when will both these trains meet?
A) 4 hours
B)5 hours
C)6 hours
D)4.5 hours
Answer: B
Explanation:
Time = Distance between stations / Relative Speed
= 450 / (54+36)
=450 / 90
= 5 hours.
Here the correct answer is option B
Directions (22-25) : Pie chart shows the various expenditures of a person on different items. Total expenditure Rs36000.
Que 22. What is the expenditure on Medicines?
A)9000
B)4320
C)4680
D)5260
Answer: B
Explanation:
Expenditure on medicines =12% of 36000 = 4320.
Here the correct answer is option B
Que 23. The ratio of expenditure on clothes and loans?
A) 3 : 8
B) 13 : 33
C) 6 : 11
D) 4 : 11
Answer: B
Explanation:
Required ratio = 13% of 36000 : 33% of 36000
= 13 : 33.
Here the correct answer is option B
Que 24. Total expenditure on study and food?
A)15120
B)12780
C)14240
D)13000
Answer: A
Explanation:
Study + food = 25% + 17% of total expenditure.
= 42% of Rs36000.
= Rs15120.
Here the correct answer is option A
Que 25. Sum of which 2 have the maximum expenditure?
A) food and clothes
B) medicines and loan
C) Medicines and food
D) Food and study
Answer: B
Explanation:
Medicine and Loan
= 45% of Rs 36000
Here the correct answer is option B
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