Averages Quiz – 1

Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.

 Required sale = Rs.[(6500 x 6) - 34009]

= Rs. (39000 - 34009) 

= Rs.  4991.

Average of 20 numbers = 0. 

 Sum of 20 numbers = (0 * 20) = 0. 

 It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (- a).

Let the first number be x,

Then, sum of the four numbers = x + 4x = 5x.

so,  5x/4 = 60 or x = (60 * 4) / 5 = 48.

Let the total score be x.

(x + 92 - 85) / 8 = 84.

So,  x + 7 = 672

x = 665

 The total previous score  = 16x

Total +New score = 16x+85

Total score with new average = 17(x+3)

16x + 85 = 17(x + 3)

x = 34 + 3 = 37

Total sum of ages before teacher joins = 36*14

                        Total sum of ages after teacher joins = 37*15

Age of teacher  = Difference of (37*15-36*14)

    = 51

Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.

or  137 + x = 144 or x = 144 - 137 = 7.

Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]

                                                   = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.

Required average = (9.2 / 2) =  4.6.

Let the numbers are x1,x2,x3…….x75

By hypothesis ,(x1+x1+......x75) / 75 = 35

 

Mean od new number   = (x1+5)+(x2+5)......(x75+5) / 75

        = (x1+x2+......x75 + 5*75) / 75

      =  35+5

      =  40

Average speed = (2xy) /(x + y) km/hr

                      = (2 * 50 * 30) / (50 + 30) km/hr.

                         37.5 km/hr