SSC-CPO 2020 Quantitative Aptitude

Practice subject-wise previous year questions

Question 26

Arithmetic

If x 2 - 5x + 1 = 0, then the value of \(\left(x^4 + \frac 1 {x^2}\right) \div \left(x^2 + 1\right)\)  is:

Question 27

Arithmetic

The length of the shadow of a vertical pole on the ground is 18 m. If the angle of elevation of the sun at that time is θ, such that  \(\cos \theta = \frac {12}{13}\) , then what is the height (in m) of the pole?

7.5

Question 28

Arithmetic

If A is \(\frac 1 6\)  of C, and B is twice of A, and the average of A, B and C is 30, then the difference between A and C is:

Question 29

Arithmetic

The value of \(\frac {0.325 \times 0.325 + 0.175 \times 0.175 + 25 \times 0.00455}{5 \times 0.0065 \times 3.25 - 7 \times 0.175 \times 0.025} - \frac {0.5}{1.5}\)  is:

-3

-1

Question 30

Arithmetic

The monthly salary of a person was Rs. 50,000. He used to spend on Family expenses (E), Taxes (T), Charity (C), and the rest were his savings. E was 60% of the income, T was 20% of E, and C was 15% of T. When his salary got raised by 40%, he maintained the percentage level of E, but T becomes 30% of E and C becomes 20% of T. The difference between the two savings (in Rs.) is:

220

250

130

128

Question 31

Arithmetic

When operated separately, pipe A takes 5 hours less than pipe B to fill a cistern, and when both pipes are operated together, the cistern gets filled in 6 hours. In how much time (in hours) will pipe B fill the cistern, if operated separately?

Question 32

Arithmetic

The given pie chart shows the percentage distribution of 450 employees in an organisation. Study the pie chart and answer the question that follows. If 60% of the employees in department E are females, how many male employees are there in that department?

Question 33

Arithmetic

A sum of Rs. 8,200 was divided among A, B and C in such a way that A has Rs. 500 more than B, and C has Rs. 300 more than A. How much was A's share (in Rs.)?

2,800

2,300

3,100

2,000

Question 34

Arithmetic

Asha and Suman's mud forts have heights 9 cm and 16 cm. They are 24 cm apart. How far (in cm) are the fort tops from each other?

Question 35

Arithmetic

The given pie chart shows the percentage distribution of 450 employees in an organisation. Study the pie chart and answer the question that follows. What is the number of employees working in department B?

Question 36

Arithmetic

Two pipes can fill a tank in 15 hours and 4 hours, respectively, while a third pipe can empty it in 12 hours. How long (in hours) will it take to fill the empty tank if all the three pipes are opened simultaneously?

30 / 7

20 / 7

50 / 7

15 / 7

Question 37

Arithmetic

A and B started a business investing amounts of Rs. 92,500 and Rs. 1,12,500 respectively. If B's share in the profit earned by them is Rs. 9,000, what is the total profit (in Rs.) earned by them together?

19,000

20,000

21,240

16,400

Question 38

Arithmetic

Rice is now being sold at Rs. 29 per kg. During the last month, its cost was Rs. 25 per kg. By how much percentage should a family reduce its consumption, so as to keep the expenditure the same as before? (correct to nearest integer)

13%

15%

14%

12%

Question 39

Arithmetic

If the annual rate of simple interest increases from 11% to \(17 \frac 1 2\%\) , a person's yearly income increases by Rs. 1,071.20. The principal amount invested (in Rs.) is:

16,480

19,120

17,250

10,710

Question 40

Arithmetic

The two parallel sides of a trapezium are 27 cm and 13 cm, respectively. If the height of the trapezium is 7 cm, then what is its area in m 2 ?

140

1.4

0.014

0.14

Question 41

Arithmetic

PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that &ang;APB = 100°, then &ang;OAB is equal to:

45°

70°

50°

35°

Question 42

Arithmetic

A 9 cm solid metallic cube and a solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted and recast into a single cube. What is the total surface area (in cm 2 ) of the new cube?

1362

865

2744

1176

Question 43

Arithmetic

A bus covers a 60-kilometre distance in 1 hour 15 minutes, whereas the same distance is covered by a car in 45 minutes. What is the ratio of the speed of the bus to the speed of the car?

5 : 3

1 : 3

3 : 1

3 : 5

Question 44

Arithmetic

Let ΔABC ~ ΔRPQ and  \(\frac {ar (\Delta ABC)}{ar(\Delta RPQ)} = \frac 4 9\) . If AB = 3 cm, BC = 4 cm and AC = 5 cm, then PQ (in cm) is equal to:

4.5

Question 45

Arithmetic

If sec3x = cosec(3x - 45°), where 3x is an acute angle, then x is equal to:

35°

45°

22.5°

27.5°

Question 46

Arithmetic

The given histogram shows the frequency distribution of the speed of cars passing through at a particular spot on a highway. Study the graph and answer the question that follows. What percentage of cars were running with a speed of less than or equal to 70 km/h?

30%

51.25%

60%

45.75%

Question 47

Arithmetic

The remainder when 75 × 73 × 78 × 76 is divided by 34 is:

Question 48

Arithmetic

If the area of a square is decreased by 19%, then the diagonal of the square is decreased by:

15%

10%

12%

Question 49

Arithmetic

The value of \(3 \frac 1 3 \div 2 \frac 1 2 \rm\;of\;1 \frac 3 5 + \left(\frac 3 8 + \frac 1 7 \times 1 \frac 3 4\right)\) is:

35 / 24

55 / 24

5 / 24

25 / 24

Question 50

Arithmetic

If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of x 3 + y 3 + z 3 + xyz is:

1225

1441

577

361

1 2 3 4 5 6 7 8 9 10 11 12

If x 2 - 5x + 1 = 0, then the value of \(\left(x^4 + \frac 1 {x^2}\right) \div \left(x^2 + 1\right)\) &nbsp;is:

The length of the shadow of a vertical pole on the ground is 18 m. If the angle of elevation of the sun at that time is &theta;, such that&nbsp; \(\cos \theta = \frac {12}{13}\) , then what is the height (in m) of the pole?

If A is \(\frac 1 6\) &nbsp;of C, and B is twice of A, and the average of A, B and C is 30, then the difference between A and C is:

The value of \(\frac {0.325 \times 0.325 + 0.175 \times 0.175 + 25 \times 0.00455}{5 \times 0.0065 \times 3.25 - 7 \times 0.175 \times 0.025} - \frac {0.5}{1.5}\) &nbsp;is:

When operated separately, pipe A takes 5 hours less than pipe B to fill a cistern, and when both pipes are operated together, the cistern gets filled in 6 hours. In how much time (in hours) will pipe B fill the cistern, if operated separately?

The given pie chart shows the percentage distribution of 450 employees in an organisation. Study the pie chart and answer the question that follows. If 60% of the employees in department E are females, how many male employees are there in that department?

A sum of Rs. 8,200 was divided among A, B and C in such a way that A has Rs. 500 more than B, and C has Rs. 300 more than A. How much was A's share (in Rs.)?

Asha and Suman's mud forts have heights 9 cm and 16 cm. They are 24 cm apart. How far (in cm) are the fort tops from each other?

The given pie chart shows the percentage distribution of 450 employees in an organisation. Study the pie chart and answer the question that follows. What is the number of employees working in department B?

Two pipes can fill a tank in 15 hours and 4 hours, respectively, while a third pipe can empty it in 12 hours. How long (in hours) will it take to fill the empty tank if all the three pipes are opened simultaneously?

A and B started a business investing amounts of Rs. 92,500 and Rs. 1,12,500 respectively. If B's share in the profit earned by them is Rs. 9,000, what is the total profit (in Rs.) earned by them together?

Rice is now being sold at Rs. 29 per kg. During the last month, its cost was Rs. 25 per kg. By how much percentage should a family reduce its consumption, so as to keep the expenditure the same as before? (correct to nearest integer)

If the annual rate of simple interest increases from 11% to \(17 \frac 1 2\%\) , a person's yearly income increases by Rs. 1,071.20. The principal amount invested (in Rs.) is:

The two parallel sides of a trapezium are 27 cm and 13 cm, respectively. If the height of the trapezium is 7 cm, then what is its area in m 2 ?

PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that &ang;APB = 100&deg;, then&nbsp;&ang;OAB is equal to:

A 9 cm solid metallic cube and a solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted and recast into a single cube. What is the total surface area (in cm 2 ) of the new cube?

A bus covers a 60-kilometre distance in 1 hour 15 minutes, whereas the same distance is covered by a car in 45 minutes. What is the ratio of the speed of the bus to the speed of the car?

Let &Delta;ABC ~&nbsp;&Delta;RPQ and&nbsp; \(\frac {ar (\Delta ABC)}{ar(\Delta RPQ)} = \frac 4 9\) . If AB = 3 cm, BC = 4 cm and AC = 5 cm, then PQ (in cm) is equal to:

If sec3x = cosec(3x - 45&deg;), where 3x is an acute angle, then x is equal to:

The given histogram shows the frequency distribution of the speed of cars passing through at a particular spot on a highway. Study the graph and answer the question that follows. What percentage of cars were running with a speed of less than or equal to 70 km/h?

The remainder when 75 &times; 73&nbsp;&times; 78&nbsp;&times; 76 is divided by 34 is:

If the area of a square is decreased by 19%, then the diagonal of the square is decreased by:

The value of \(3 \frac 1 3 \div 2 \frac 1 2 \rm\;of\;1 \frac 3 5 + \left(\frac 3 8 + \frac 1 7 \times 1 \frac 3 4\right)\) is:

If x + y + z = 19, xyz = 216 and xy + yz + zx = 114, then the value of x 3 + y 3 + z 3 + xyz is:

If x 2 - 5x + 1 = 0, then the value of \(\left(x^4 + \frac 1 {x^2}\right) \div \left(x^2 + 1\right)\) is:

The length of the shadow of a vertical pole on the ground is 18 m. If the angle of elevation of the sun at that time is θ, such that \(\cos \theta = \frac {12}{13}\) , then what is the height (in m) of the pole?

If A is \(\frac 1 6\) of C, and B is twice of A, and the average of A, B and C is 30, then the difference between A and C is:

The value of \(\frac {0.325 \times 0.325 + 0.175 \times 0.175 + 25 \times 0.00455}{5 \times 0.0065 \times 3.25 - 7 \times 0.175 \times 0.025} - \frac {0.5}{1.5}\) is:

PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that &ang;APB = 100°, then &ang;OAB is equal to:

Let ΔABC ~ ΔRPQ and \(\frac {ar (\Delta ABC)}{ar(\Delta RPQ)} = \frac 4 9\) . If AB = 3 cm, BC = 4 cm and AC = 5 cm, then PQ (in cm) is equal to:

If sec3x = cosec(3x - 45°), where 3x is an acute angle, then x is equal to:

The remainder when 75 × 73 × 78 × 76 is divided by 34 is: