Mathematics (Sub Inspector)

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.

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

( 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

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

 

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 %

 

         

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
 
 

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

 

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                    
 

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

 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

 

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                    

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

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