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Mathematics (Sub Inspector)

Description: These are MCQ questions and are interesting,based on simple school mathematics
Number of Questions: 16
Created by:
Tags: MCQ Time and Work Mensuration Single Variable Percentages Profit & Loss Linear Equations Ratio/Proportion & Variation Volume LCM/HCF Arithmetic
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A soft drink manufacturing company wanted to arrange 160 bottles of soft drinks in a square carton, but 16 bottles were left over. How many bottles were there in each row?

  1. 4

  2. 12

  3. 164

  4. 144

Show answer
Correct Option: B
Explanation:

Let there be 'a' bottles in each row.
number of rows=a
 
so number of bottles are = a2
It is given that after arranging bottles in the form of square,16 were left over
Total number of bottles = a2 + 16But total number of bottles are 160

then    a2 +16  =160 a2 = 160 - 16 a2 = 144 a = 12 There were 12 bottles in each row.

A man had Rs. x, from which he spent Rs. 6. If twice the amount left with him is Rs. 86, find x.

  1. Rs. 46

  2. Rs. 49

  3. Rs. 178

  4. Rs. 37

  5. Rs. 40

Show answer
Correct Option: B
Explanation:

 
The money the man had  Rs. xMoney spent by him =Rs.6Money left with him = Rs.( x - 6 ) According to the question twice thhe money left with him is Rs. =86 2(x - 6) = 86
2x - 12 = 86
2x = 86 + 12
2x = 98
x = 98/2
x = 49

The area of a square is 2304 m2. Its one side is equal to the breadth of a rectangle and its length is double of its breadth. Find the perimeter of the rectangle.

  1. 288 m

  2. 3456 m

  3. 663552 m

  4. 4608 m

Show answer
Correct Option: A
Explanation:

 Area of square is 2304 m2 one side of square is square root of 2304
                          =48 m
 
 
one side of square is equal to the breadth of rectangle

so breadth of rectangle is  =48 m

length of rectangle is double of breadth=2x48                                                                       =96m
 
perimeter of rectangle = 2 x (l + b )                                       =2x ( 48 + 96 )
                                        = 2 x 144                                         = 288 m

 

A and B can do a piece of work in 6 days. B and C can do it in 7½ days. C and A can do it in 10 days. In how many days will B alone finish it?

  1. 30 days

  2. 10 days

  3. 15 days

  4. 1/10 days

Show answer
Correct Option: B
Explanation:

( A + B ) 's  1 day work  = 1 / 6( B + C ) 's 1 day work = 2 / 15       ( 7 1/2 = 15 /2 ) ( C + A )'s 1 day work = 1/ 10By adding

( A+ B ) + ( B + C ) + ( C + A ) 's 1 day work = 1/ 6 + 2/15 + 1/10  (A + B + B + C + C + A) 's 1 day work = 1/ 6 + 2/15 + 1/10  ( 2A + 2B + 2C ) 's 1 day work = 1/6 + 2/15 + 1/10 2 ( A + B + C ) 's 1 day work = (5 + 4 + 3) /30 = 12/30 = 6 /15 (A + B + C )'s 1 day work = 6/15 x 2 = 6/30

( A + B + C ) 's 1 day work - ( C + A ) 's 1 day work =                                  6/30 - 1/10                                 = 6 - 3 /30                                = 3/30                                  = 1 /10 B1 day work is 1/10 B can complete whole work in  1 / 1/10 = 10 days

If 500 ml solution of lemonade contains 40% lemon juice, how much more lemon juice should be added to make it 60%? .

  1. 800 ml

  2. 600 ml

  3. 250 ml

  4. 120 ml

Show answer
Correct Option: C
Explanation:

Quantity of lemon juice in 100 ml = 40mlQuantity of lemon juice in 1 ml = 40/100Quantity of lemon juice in 500 ml = 40/100 x 500 = 200 mlwhen we want to make it 60 % we have to add more lemon juice .Suppose x ml of lemoon juice is added now 

Quantity of lemonade will be =( 500 + x) ml  Quantity of lemon juice will be = ( 200 + x ) ml Now quantity of lemon juice in  ( 500 + x ) ml is ( 200 + x )  Quantity of lemon juice in 1 ml is ( 500 + x ) / ( 200 + x )  Quantity of lemon juice in 100 ml is=                                                  { ( 500 + x ) / ( 200 + x ) } x 100}%The % of lemon juice is 60%(200 + x) / ( 500 + x ) x 100 = 60(200 + x )100 = 60 x ( 500 + x )   20000 + 100 x = 30000 + 60 x   100 x - 60 x = 30000 - 20000  40 x = 10000

     x = 10000 /40

    x = 250 ml

 

A milkman purchased milk at Rs. 4 per litre and mixed 20% water in it. Find the gain % if the diluted milk is sold at Rs. 5 per litre.

  1. 200%

  2. 50%

  3. 20%

  4. 33.33%

Show answer
Correct Option: B
Explanation:

Let the quantity of milk purchased  = 100 ml  so the cost of milk at the rate of Rs. 4 per iltre is = 4 x 100 =                                                                                                    Rs400                     Quantity of water added 20%                         it means 20 ml of water in 100 ml                      Now quantity of milk after adding water = 100 + 20                                                                                         = 120 ml      Selling price of  milk at the rate of Rs 5 is 5 x 120= Rs.600

            Selling price > cost price            so gain      Gain = Selling Price - Cost Price               = Rs. 600 - Rs. 400                =Rs. 200       Gain %   =   Gain /Cost Price x 100                        = 200 / 400 x 100                              =      50 %

 

Egyptians were the first to use fractions. However, they used fractions with one as numerator. They would write 3/8 as 1/4 and 1/8. What would they write for 9/20?

  1. 1/20

  2. 1/5, 1/20, 1/5

  3. 1/20, 1/10

  4. 1/4, 1/5

Show answer
Correct Option: B
Explanation:

As given 3/8 is 1/4 and 1/8
 
means 1/4 + 1/8 =  (2+1) / 8 = 3/8

so if we add,we get

 
1/5 + 1/20 + 1/5 = (4+1+4)/20 = 9/20
         

The ratio of surface areas of 2 cubes is 1 : 9. Find the ratio of their volumes.

  1. 1 : 729

  2. 3 : 27

  3. 1 : 27

  4. 1 : 9

Show answer
Correct Option: C
Explanation:

Let the side of one cube is 2 cmThen surface area = 6 l2 = 6 x 2 x 2 = 24 cm2  Other cube's surface area will be 9 x 24 = 216 cm2

( as they are in ratio of 1: 9 ) 

now      6 l2 = 216              l2 = 216 / 6

               l2 = 36               l = 6volume of first cube  = side x side x side                                      = 2 x 2 x 2 = 8 cm3                                      volume of other cube = 6 x 6 x 6  = 216 cm3              Ratio = 8 / 216 = 1 / 27

       so ratio will be 1 : 27    

Find the smallest number that should be added to 1500, so that the sum is exactly divisible by 18, 20 and 24.

  1. 60

  2. 2

  3. 360

  4. 300

Show answer
Correct Option: D
Explanation:

The smallest number that is exactly divisible by18,20 and 24.we take their lowest common mutipleL.C.M. of 18, 20, 24 is 

2 x 2 x 2 x 3 x 3 x 5 =360Number just greater than1500 is divisible by 360 1500 / 360=Quotient = 4 Remainder = 60 Number which will be added 1500+ ( 360 - 60 ) 1500 + 300 = 1800 Required number is 300 when added to1500 will be exactly divisible by18,20,24 As we division is repeated subtraction (1)  1500 - 360 = 1140(2)  1140 - 360 = 780(3) 780 - 360 = 420(4) 420 - 360 = 60

To make last 5th set we will add 300 to 60 to bring 0 60 + 300 = 360(5) 360 - 360  = 0 

so number 300 which will be added to 1500

 

In an isosceles triangle, two equal sides are each 8 cm less than three times the third side. The perimeter of triangle is 33 cm. What is the measurement of equal sides?

  1. 7 cm

  2. 8.2 cm

  3. 13 cm

  4. 5 cm

Show answer
Correct Option: C
Explanation:

Let the third side is = x 

 Three times of x is = 3x  8 cm less than 3 times = ( 3x - 8 ) cm  two equal sides are = ( 3x - 8 ) cm Perimeter of of triangle is sum of all sides                   ( 3x - 8 ) + ( 3x -  8 ) + x = 33                     3x - 8 + 3x - 8 + x = 33                                        3x + 3x + x - 8 - 8 = 33                                         7x - 16 = 33                                             7x = 33 + 16                                           7x = 49                              x = 49 / 7                                         x = 7 cm                        Third side is 7 cm                    Two equal sides are =( 3 x 7 ) - 8                                               = 21 - 8                                                = 13 cm                                                    Two equal sides measure = 13 cm each                      

Find the product of the smallest 2-digit number and the difference between the original number and the new number if digits 2 and 5 of the number 32576 are interchanged.

  1. 290484

  2. 27000

  3. 352760

  4. 2700

Show answer
Correct Option: B
Explanation:

Smallest 2-digit number = 10

Original number = 32576New number after inter changing the digits = 35276  Difference = 35276 - 32576 = 2700  Product of smallest 2 digit number and difference is 2700 x 10                                                                                                                                                                         =27000

Three colours of chart papers: green, red and blue have to arranged in such a way that all the chart papers are stored colourwise and height of each bundle is the same. The number of green chart papers is 96, of red chart papers is 240 and of blue chart papers is 336. Thickness of each chart paper is the same. Determine the number of bundles of green, red and blue, respectively.

  1. 35, 14, 10

  2. 48, 48, 48

  3. 2, 5, 7

  4. 32, 80, 112

Show answer
Correct Option: C
Explanation:

In order to arrange chart papers as required we have to find
 
the largest number that divides 96,240 and 336.Clearly such
number is their H.C. F.
96  = 2 x 2 x 2 x 2 x 2 x 3
 
240 = 2 x 2 x 2 x 2 x 3 x 5
 
336 = 2 x 2 x 2 x 2 x 3 x 7
 
H.C.F. = 2 x 2 x 2 x 2 x 3 = 48
 
 
Hence there must be 48 chart papers in each bundle
 
 Number of green chart paper bundles = 96/48 = 2

Number of red chart paper bundles = 240/48 = 5 Number of blue chart paper bundles = 336/48 = 7

 

A shopkeeper bought 10 water coolers at the rate of Rs. 4200 each. He sold them at a profit equal to the selling price of 3 coolers. Find the selling price of one water cooler.

  1. Rs. 600

  2. Rs. 323.07

  3. Rs. 3230.76

  4. Rs. 6000

Show answer
Correct Option: D
Explanation:

Let the selling price of  one water cooler is Rs.x              Selling price of 3 water coolers = Rs 3x                    Profit =  selling price of 3 coolers

                     therefore    profit  = Rs 3x              Cost of one water cooler = Rs. 4200                  Cost of 10 water coolers = 4200 x 10                                                             = Rs. 42000               Selling price = cost price + profit

          Selling price of 10 water coolers = Rs. 10 x          Selling of 10 water coolers = 42000 + 3x                       10 x  = 42000 + 3x                                           10x - 3x = 42000                          7x = 42000

                            x = 42000 / 7                             x = 6000so selling price of one water cooler is Rs. 6000                    

Arun sold an article at a profit of 10%. If he had purchased it at 10% less and sold it for Rs. 28 more, he would have gained 30%. Find the cost price of the article.

  1. Rs. 35

  2. Rs. 400

  3. Rs. 360

  4. Rs. 89

Show answer
Correct Option: B
Explanation:

Let the cost price of article is  = Rs. 100Profit % = 10 %Profit = 10/100 x 100 = Rs. 10Selling price = Cost Price + Profit                       = 100 + 10                         = Rs. 110If he had  purchased it at 10 %less 10% of Rs. 100 10/100 x 100 =Rs. 10 then cost Price will be = 100 - 10 = Rs. 90 He sold it at 30% Profit Profit=30% of Rs. 90              = 30/100 x 90                = Rs. 27 Selling Price = Cost Price + Profit

                             = 90 + 27

                                = Rs. 117 Difference in selling Price =  117 - 110 = Rs. 7

If difference in Selling Price is Rs 7 then Cost Price is =Rs. 100If difference in Selling Price is Rs.1then Cost Price is 100/7If difference in Selling Price is Rs.28 then Cost Price =                                                                                =  100/7 x 28                                                                                  = 400      so Cost Price of article is Rs. 400

The volume of a petrol tank is twice that of another. If we draw 25 litres from the first tank and add to the other tank, then volume in each tank will be the same. Find the volume of tank which has more petrol in it.

  1. 100 litres

  2. 50 litres

  3. 150 litres

  4. 25 litres

Show answer
Correct Option: A
Explanation:

Let the volume of the tank which has less petrol is x litres
 
other tank's volume which has more petrol  = 2x  litres
 
If we draw 25 litres from the tank which has more petrol and add to other tank which has less petrol then volume will be same,equation is 
 
                           2x - 25 = x + 25
 
 
                             2x- x  = 25 + 25 
 
                                    x   =  50
 
Volume of tank which has more petrol will be twice of the other, i.e. 2 x 50 = 100 litres.

The top of a table is covered wth 25 squares of equal size. The side of a square is 3 cm. What is the area of the table top (in cm2)?

  1. 300

  2. 75

  3. 225

  4. 5625

  5. ------------------------

Show answer
Correct Option: C
Explanation:

Side of square = 3 cm Area of square  = side x side                       = 3 x 3 =   9 cm2

Number of squares = 25Area covered by one square = 9 cm2  so Area of table top is 25 x 9 = 225 cm2

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