SSC GD Constable 2015 Question Paper - Morning Shift - Elementary Mathematics Questions and Answers

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SSC GD Constable 2015 Question Paper - Morning Shift : Elementary Mathematics

1. 16 men are able to complete a piece of work in 12 days working 14 hours a day. How long will 28 men, working 12 hours a day, take to complete the work ?
[A] 7 days
[B] 10 days
[C] 8 days
[D] 6 days

Answer: C. 8 days

Explanation:

Formula:

M1D1H1 = M2D2H2

Where M = number of Men, D = number of days and H = number of hours

Given,

M1 = 16, D1 = 12, H1 = 14, M2 = 28, H2 = 12 and D2 = ?

D2 = (16 x 12 x 14) / (28 x 12)

= 8 days

Then, 28 men working 12 hours a day, take to complete the work in 8 days.
2. A certain sum amounts to Rs. 1725 at 15% per annum at simple interest and Rs. 1800 in the same time at 20% per annum at simple interest. Find the sum.
[A] Rs. 1700
[B] Rs. 1500
[C] Rs. 1650
[D] Rs. 1200

Answer: B. Rs. 1500

Explanation:

Let the principle be Rs. x

If rate of simple interest per annum = 15%, amount = Rs. 1725
And rate of simple interest per annum = 20%, amount = Rs. 1800

Then, 5% of principle = 1800-1725 = Rs. 75

Therefore, 100% priniciple = 75 x 100/5
                                          = 75 x 20
                                           => Rs. 1500

Then, the principle is Rs. 1500
3. A dealer marks his goods 20% above cost price and allows a discount of 10% to his customers. His gain percentage is ?
[A] 6%
[B] 7%
[C] 8%
[D] 9%

Answer: C. 8%

Explanation:

Let the cost price of goods = Rs. 100
A dealer marks his goods 20% above cost price.

Then, the price of goods = 100 + 100 x 20/100
                                        = 100+20
                                        = 120

He gave 10% discount,
then selling price = 120 - 120 x 10/100
                            = 120 - 12
                            = Rs. 108

Gain% = 108 - 100
            = 8%

Then, his gain % is 8
4. Raja can do a piece of work in 20 days while ramesh can finish it in 25 days. Ramesh started working and Raja joined him after 10 days. The whole work is completed in ?
[A] 20 days
[B] 16 2/3 days
[C] 15 days
[D] 18 days

Answer: B. 16 2/3 days

Explanation:

Raja can do a piece of work = 20 days
Therefore, Raja can do a piece of work in a day = 1/20

Ramesh can do a piece of work = 25 days
Therefore, Ramesh can do a piece of work in a day = 1/25

Raja and Ramesh can do together work in a day = 1/20 + 1/25
                                                                             => 9/100

Then, Raja and Ramesh can do together work = 100/9 days

Ramesh can do a work in 10 days = 10/25

Remaining work = 1-10/25
                          => 3/5

Then, Raja & Ramesh can do complete remaining work = 100 x 3/5 x 9
                                                                                        => 20/3

Therefore, the whole work is complete = 10 + 20/3
                                                             => 50/3 days
5. 1008 divided by which single digit number gives a perfect square ?
[A] 7
[B] 8
[C] 9
[D] 4

Answer: A. 7

Explanation:

Take option (1),
1008 divide by 7 = 1008/7 = 144
144 is a square of 12

Now, take option (2)
1008 divide by 8 = 1008/8 = 126
126 is not a square of any number.

Take option (3)
1008 divide by 9 = 1008/9 = 112
112 is not a square of any number.

Take option (4),
1008 divide by 4 = 1008/4 = 252
252 is not a square of any number.

Hence, the answer is 7
6. A right circular cone of height 20 cm and base radius 15 cm is melted and casted into smaller cones of equal sizes of height 5 cm and base radius 1.5 cm. The number of casted cones are ?
[A] 100
[B] 300
[C] 150
[D] 400

Answer: D. 400

Explanation:

The height of a cone = 20cm and radius of cone = 15 cm

Volume of cone = 1/3(πr2h)

Then, volume = 1/3(π x 152 x 20)
=> 1500π cm3

The height of small cone = 5cm
Radius of small cone = 1.5 cm

Volume of small cone = 1/3(5 x 1.5 x 1.5 x π)

=> 3.75π cm3

Then the number of small cones = 1500π / 3.75π => 400

Hence the number of casted cones = 400
7. A student starting from his house walks at a speed of 2 1/2 km/hour and reaches his school 7 minutes late. Next day starting at  the same time he increases his speed by 1 km/hour and reaches 6 minutes early. The distance between school and his house is ?
[A] 4 km
[B] 6 km
[C] 3 1/2 km
[D] 1 3/4 km

Answer: D. 1 3/4 km

Explanation:

Let the distance between school and his house be x km

According to question,

x(5/2) + 6/60 = x(5/2 + 1) - 6/60
2x/5 + 1/10 = 2x/7 - 1/10
(7 * 2x - 5 * 2x)/35 = -2/10
(14x - 10x)/35 = -1/5
4x = -7
x = -7/4

As, distance is never in negative

Hence, x = 7/4

Hence, the distance between the school and house is 1 3/4 km
8. The mean proportion of 1.21 and 0.09 is ?
[A] 3.03
[B] 0.03
[C] 0.33
[D] 3.3

Answer: C. 0.33

9. The value of .000441 is equal to ?
[A] 0.21
[B] 0.021
[C] 0.0021
[D] 0.00021

Answer: B. 0.021

Explanation:

(0.000441)1/2 = (0.021 x 0.021)1/2

                       => 0.021
10. A batsman makes a score of 87 runs in the 17th inning and thus increased his average by 3. Find his average after 17th inning.
[A] 90
[B] 84
[C] 39
[D] 87

Answer: C. 39

Explanation:

Let the average after 17th innings = x
Then, the average after 16th innings = x-3

According to question,

16(x-3) + 87 = 17x
16x - 48 + 87 = 17x
16x + 39 = 17x
17x - 16x = 39
x = 39

Then, the average after 17th innings is 39

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