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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(πr
2h)

Then, volume = 1/3(π x 15
2 x 20)
=> 1500π cm
3

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 cm
3

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

11.A fruit merchant makes a profit of 25% by selling mangoes at a certain price. If he charges rs. 1 more on each mango, he would gain 50%. At first the price of one mango was?
[A] Rs. 6
[B] Rs. 4
[C] Rs. 7
[D] Rs. 5
Answer: B. Rs. 4
Explanation:
Let the price of a mango = Rs. x
Profit = 25%

Then, the selling price of a mango = 125x / 100
                                                        => 5x / 4

According to question,
 

150x/100 - 125x/100 = 1
6x/4 = 5x/4 = 1
(6x - 5x)/4 = 1
x/4 = 1

x = 4

Then, the first price of a mango is Rs. 4

12.A seller increases the cost price of an article by 30% and fixed the marked price as Rs. 286. But during sale he gave 10% discount to the purchaser. Percentage of profit will be?
[A] 15
[B] 20
[C] 17
[D] 10
Answer: C. 17
Explanation:
Let the cost price of goods = Rs. 100
A dealer marks his goods 30% above cost price.

Then, the price of goods = 100 + 100 * 30/100
                                        => 100+30
                                        => 130

He gave 10% discount,
Then, selling price = 130 - 130 * 10/100
                              => 130 - 13
                              => Rs. 117

Gain% = 117 - 100
           => 17%

Then, gain% = 17%

13.An item was sold for rs. 3600 at 25% discount. Its marked price was?
[A] Rs. 4500
[B] Rs. 4800
[C] Rs. 2700
[D] Rs. 2880
Answer: B. Rs. 4800
Explanation:
The selling price of an item = Rs. 3600
Discount = 25%

Then, the marked price of an item = 3600 x 100(100-25)
=> 3600 x 100/75
=> 3600 x 4/3
=> 1200 x 4
=> Rs. 4800

Then, the marked price of an item = Rs. 4800

14.If  the cost of an article is Rs. P after two successive reductions of 20% and 25%, the original price of an article was?
[A] Rs. 4P/5
[B] Rs. 3P/5
[C] Rs. 5P/3
[D] Rs. 5P/4
Answer: B. Rs. 3P/5
Explanation:
The cost price of an article = Rs. P

Successive reductions = 20% and 25%
Then, successive reduction = 20 + 25 - 20 x 25/100
=> 45 - 5
=> 40%

Then, the original price = P - P x 40/100
=> P -2P/5
=> (5P - 2P)/5
=> Rs. 3P/5

15.A plane can cover 6000 km in 8 hours. If the speed is increased by 250 km/h, then the time taken by the plane to cover 9000 km is?
[A] 5 hours
[B] 8 hours
[C] 6 hours
[D] 9 hours
Answer: D. 9 hours
Explanation:
A plane can cover 600 km = 8 hours
Then, the speed of a plane = 6000/8
=> 750 km/hr

If the speed increased by 250 km/hr
Then, the speed of a plane = 750 + 250 = 1000 km/hr

Time taken by plane to cover 9000 km = 9000/1000
=> 9 hrs

Then, the time taken by plane to cover 9000 km is 9 hrs.

16.A solid right prism  made of iron has cross section of a triangle of sides 5cm, 10cm, 13cm and of height 10cm. If one cubic cm of iron weights 7g, then the weight of the prism is?
[A] 137.32 gram
[B] 1100.68 gram
[C] 1570.8 gram
[D] 1470.8 gram
Answer: No Answer Available, Suggest your answer below!
 0  1
17.A sum of Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest. If the rate of interest is increased by 4% what amount will the same sum become in 3 years?
[A] Rs. 1052
[B] Rs. 1042
[C] Rs. 1024
[D] Rs. 1025
Answer: A. Rs. 1052
Explanation:
A sum of Rs. 800 becomes Rs. 956 in 3 years at a certain rate of simple interest.

Then, the simple interest of three years = 956-800 => 156 Rs.

Simple Interest = (P x t x r)/100

Then,
 
156 = (800 x 3 x r)/100
r = 156/3 * 8
 
r = 6.5%

If rate of interest is increased by 4%
Then, the rate of interest = 6.5+4 = 10.5%

Now, simple interest = 800 x 10.5 x 3 /100

=> 24 x 10.5
=> Rs. 252

Then, the amount will be in 3 years = 800 + 252 => 1052

18.A shopkeeper in order to clear his old stock of T.V sets, offer 12% discount on the T.V. sets. If the marked price of a T.V. set is Rs. 6500, the selling price of the T.V. set is?
[A] Rs. 5700
[B] Rs. 6000
[C] Rs. 5720
[D] Rs. 5400
Answer: C. Rs. 5720
Explanation:
The marked price of a T.V set = Rs. 6500
Discount = 12%

Then, selling price of a T.V. set = 6500 x (100-12)/100
=> 6500 x 88/100
=> 65 x 88
=> Rs. 5720

Then, the selling price of a T.V. set is Rs. 5720

19.Average income of 'A' and 'B' is Rs. 200 and average income of 'C' and 'D' is Rs. 250. The average income of A,B,C and D is?
[A] Rs. 200
[B] Rs. 225
[C] Rs. 125
[D] Rs. 106.25
Answer: B. Rs. 225
Explanation:
The average income of 'A' and 'B' = Rs. 200
Then, the total income of 'A' and 'B' = 2 x 200 => Rs. 400

The average of C and D = Rs. 250
Then the total income of C and D = 2 x 250 => Rs. 500

The total income of A, B, C and D = 400+500 = Rs. 900

The, the average income of A,B,C and D = 900/4 = Rs. 225

20.The average of 1,3,5,7,9,11,..... 25 terms is ?
[A] 125
[B] 25
[C] 625
[D] 50
Answer: B. 25
Explanation:
The sum of first n odd natural numbers = n2
Here n = 25

Then, the sum of 25 odd natural number = 25
2 => 625

Then, the average of 25 odd terms = 625/25 => 25

21.The ratio of ages of two persons is 5:9 and the age of one of them is greater than the other by 40 years. The sum of their ages in years is?
[A] 140
[B] 180
[C] 150
[D] 150
Answer: A. 140
Explanation:
The ratio of ages of two persons = 5:9
Let the age of first person be = 5x
The age of second person = 9x

The age of one of them is greater than the other by 40 years

Then, 9x - 5x = 40
=> 4x = 40
=> x = 40/4
=> x = 10

Then, age of first person = 5x10 = 50
age of second person = 9x10 = 90

So, the sum of their ages = 90+50 = 140

22.Study the data and answer the questions
The score of students of a class are given as follows.
The number of students whose IQ score is 100 and more is?
[A] 36
[B] 29
[C] 46
[D] 35
Answer: D. 35
Explanation:
The total number of students whose IQ score is 100 and more = 16+13+4+2 = 35

23.Study the data and answer the questions
The score of students of a class are given as follows.
Number of students whose IQ score is 140 is?
[A] 1
[B] 2
[C] 0
[D] underterminable form
Answer: D. underterminable form

24.The smallest number by which 243000 be divided so that the quotient is a perfect cube is?
[A] 9
[B] 27
[C] 3
[D] 1
Answer: A. 9
Explanation:
Number = 243000
If we divide by 9

Then, 243000/9 = 27000

27000 is a cube of 30

Then, the smallest number is 9 which can divide 243000 so that the quotient is a perfect cube of 30

25.In a college election, a candidate secured 62% of the votes and is elected by a margin of 144 votes. The total number of votes polled is?
[A] 800
[B] 925
[C] 1200
[D] 600
Answer: D. 600
Explanation:

Let the total number of votes polled = x

In college election, a candidate secured 62% of the votes

Then, the opposite candidate secured votes = 100-62 = 38%

Candidates elected by 144 votes

Then x * (62-38)/100 = 144

x* 24/100 = 144
x= 600

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