SSC GD Constable Exam Elementary Mathematics Number Systems: Syllabus, Questions PDF

1. A alone can complete a work in 6 days and B alone can complete the same work in 8 days. In how many days both A and B together can complete the same work?

A. days
B.  days
C.  days
D.  days

Answer ||| D

Solution |||

Let the total work be 24x (LCM of 6x and 8x).

Then, efficiency of A =  = 4x

And efficiency of B =  = 3x

Efficiency of A and B together = 4x + 3x = 7x

Time taken by A and B together to complete the work =  =  days

2. Anil, Deepak and Dinesh together can complete a work in 35 days. Anil and Dinesh together can complete the same work in 60 days. In how many days Deepak alone can complete the same work?

A. 105 days
B. 84 days
C. 96 days
D. 110 days

Answer ||| B

Solution |||

Let the total work be 420x (LCM of 35x and 60x).

Then, the efficiency of Anil, Deepak and Dinesh together =  = 12x

And efficiency of Anil and Dinesh together =  = 7x

Therefore, efficiency of Deepak = 12x – 7x = 5x

Time taken by Deepak to complete the work =  = 84 days

3. A car covers a certain distance at a speed of 48 km/hr in 14 hours. How much time it will take to cover the same distance at the speed of 84 km/hr?

A. 6 hr
B. 8 hr
C. 9 hr
D. 12 h

Answer ||| B

Solution |||

Given, Speed of car = 48 km/hr

Time = 14 Hours

Distance = Speed × Time

= 48 × 14 = 672 km

Time required in covering the same distance at the speed of 84 km/hr

=  =  = 8 hr.

4. If x : y = 5 : 4, then what will be the ratio of  ?

A. 25 : 16
B. 16 : 25
C. 4 : 5
D. 5 : 4

Answer ||| A

Solution |||

Let x is equal to ‘5a’.

Then, y = 5a ×  = 4a

Now, required 

=  = 25 : 16

5. If the length of a rectangle increases by 50% and the breadth decreases by 25%, then what will be the percent increase in its area?

A. 15%
B. 17.5%
C. 12.5%
D. 25%

Answer ||| C

Solution |||

Let the length and breadth of the rectangle are 100L and 100B respectively.

So, area of the rectangle = 100L × 100B = 10000LB

Now, new length(l1) = 100L + 50% of 100L

= 100L +  = 100L + 50L = 150L

Similarly, new breadth = (100 – 25)% of 100B

⇒ 75% of 100B = = 75B

∴ New area of the rectangle will be

= 150L × 75B = 11250LB

Increase in area = 11250LB – 10000LB = 1250LB

Required percentage increase

= = 1250/100 = 12.5%

6. A sum of Rs. 4500 is lent at compound interest. If the rate of interest is 10% per annum (interest is compounded annually), then what will be the amount after 3 years?

A. Rs. 5989.5
B. Rs. 5689.5
C. Rs. 5686.5
D. Rs. 5889.5

Answer ||| A

Solution |||

Given:

Principal = ₹ 4500, Rate of interest = 10% p.a., Time = 3 years

Compounded Amount = Principal × 

= 4500 ×  = 4500 × (1.1)³ = 4500 × 1.331

= ₹ 5989.5

7. M can complete a work in 14 days less than the time taken by L. If both M and L together can complete the same work in 24 days, then in how many days M alone can complete the same work?

A. 35 days
B. 56 days
C. 21 days
D. 42 days

Answer ||| D

Solution ||| Let time taken by L = x days

Time taken by M = (x−14) days

Now, L’s one day work + M’s one day work = 

Both M and L together can complete the same work in 24 days.

(M+N)’s one day work = 1/24

According to the question,

⇒ 

⇒ 

⇒ 48x² – 336 = x² – 14x

⇒ x² – 62x + 336 = 0

⇒ x² – 56x –6x + 336 = 0

⇒ x(x – 56) –6(x + 56) = 0

⇒ (x – 56)(x –6) = 0

⇒ x = 56 or 6

(i) If x = 56, Time taken by L = 56 days

Time taken by M = (56-14) days = 42 days

(ii) If x = 6, Time taken by L = 6 days

Time taken by M = (6−14) days = −8 days, which is not possible.

So, x ≠ 6

Hence, Time taken by M = 42 days

8.A : B = 5 : 8 and B : C = 11 : 13. If A = 110, then what is the value of C?

A. 176
B. 104
C. 208
D. 88

Answer ||| C

Solution |||

Given:

A = 110

Therefore, B = 110 ×  = 176

And C = 176 ×  = 208

9. A can complete a task in 8 days and B in 16 days respectively. If they work together for 3 days then the remaining part of the work left is:

A. 5/10
B. 9/16
C. 7/16
D. 11/16

Answer ||| C

Solution |||

Total efficiency of A and B together = (2 + 1) = 3

Work done by both in 3 days = efficiency × time = 3 × 3 = 9

Remaining work = (16 – 9) = 7

∴ Part of the work left will be = 7/16

10. The height of a cone is 24 cm and radius of its base 10 cm. If the rate of painting it is ₹ 28 cm², then what will be the total cost in painting the cone from outside?

A. ₹18880
B. ₹20820
C. ₹17660
D. ₹22880

Answer ||| D

Solution |||

ATQ, Height of the Cone ‘h’ = 24 cm

Radius of the base of the Cone ‘r’ = 10 cm

We know, Slant Height of a Cone ‘l’ = 

l = = = 26 cm

Now, the lateral surface area of a Cone- A_LSA= Πrl

A_LSA = ×10×26 cm²

And the rate of painting = ₹28 cm²

Therefore, Total cost of painting = ×10×26×28 = ₹22880

11. The diagonal of a square is 14 cm. What will be the length of the diagonal of the square whose area is double of the area of first square?

A. 
B. 
C. 28 cm
D. 

Answer ||| B

Solution |||

We know that D₁ = √2×L₁; (d=diagonal and l= length)

∴ 14 = √2 × L₁

⇒ L₁ =  cm = 7√2 cm

Area of the square = (L₁)²

= (7√2)² = 49 × 2 = 98 cm²

Area of the second square

= 2× 98 = 196 cm²

So, (L₂)² = 196

⇒ L₂ = √196 = 14 cm

Thus, D₂ = √2 × L₂;

(D₂=diagonal of second square) = √2 × 14 = 14√2 cm

12. Three cubes each of sides 7 cm are joined end to end. Find the surface area of the resulting solid.

A. 686 cm²
B. 696 cm²
C. 882 cm²
D. 782 cm²

Answer ||| A

Solution |||

Since three cubes are joined it will become a cuboid.

So, length = 7 + 7 + 7 = 21 cm,

Breadth = 7 cm and height = 7 cm

Now, required surface area of the resulting solid

= 2(lb + bh + lh)

= 2(21 × 7 + 7 × 7 + 21 × 7)

= 2(147 + 49 + 147)

= 2 × 343 = 686 cm²

13. Two numbers are in the ratio 5 : 6. If 16 is subtracted from each, the numbers will be in the ratio 3 : 4. If 8 is added to the first number and 3 is subtracted from the second, then they will be in the ratio:

A. 14 : 13
B. 16 : 15
C. 15 : 16
D. 13 : 14

Answer ||| B

Solution |||

Let the two numbers are 5x and 6x respectively.

According to the question,

⇒ 4(5x – 16) = 3(6x – 16)

⇒ 20x – 64 = 18x – 48

⇒ 20x – 18x = 64 – 48

⇒ 2x = 16

⇒ x = 16/2 = 8

∴ Two numbers are

(5 × 8) = 40 and (6 × 8) = 48

Now, 8 is added to the first number and 3 is subtracted from the second number.

(40 + 8) = 48 and (48 – 3) = 45

So, the required ratio will be –

⇒ 48 : 45 = 16 : 15

14. If A : B = 7 : 8 and B : C = 7 : 9, then what is the ratio of A : B : C ?

A. 56 : 49 : 72
B. 49 : 56 : 72
C. 56 : 72 : 49
D. 72 : 56 : 49

Answer ||| B

Solution |||

Therefore, A : B : C = 49 : 56 : 72

15. The value of [25 of 4 − 30 + (2² + 18)] is:

A. 23
B. 84
C. 92
D. 37

Answer ||| C

Solution |||

Consider [25 of 4 − 30 + (2² + 18)]

Using BODMAS

⇒ 25 of 4 − 30 + (22)

⇒ 100 – 30 + 22

= 92