Deloitte Averages Questions and Answers Quiz-1

Average = \frac{total  runs}{no.of innings} = 32
So, total = Average x no.of innings = 32 x 10 = 320
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 - 320 = 76

Prime numbers between 30 and 50 are:
31, 37, 41, 43, 47
Average of prime numbers between 30 to 50 will be
\frac{31+37+41+43+47}{5} = \frac{199}{5} = 39.8

Let the average age of the whole team by x years.

Total age of the team - Age of (captain + wicketkeeper) = Total age of the team excluding captain and wicketkeeper

11x – (26 + 29) = 9(x -1)
11x – 9x = 46
2x = 46
x = 23.
So, average age of the team is 23 years.

Average of 10 matches is 32

In 11th match, average is increased by 4 runs. Thus, average = 32 + 4 = 36

Average after 11 innings should be 36
So, Required score = 11 \times 36 - 10 \times  32 = 396 - 320 = 76

Average score of 36 boys = 40 points
Total score of 36 boys = 36 \times 40 = 1440
Average score of 44 girls = 35 points
Total score of 44 girls = 35 \times 44 = 1540
Total score of (36+44)80 Students = 1440 + 1540 = 2980 points
Average score of the whole class = \frac{2980}{80} = 37.25
Hence the required answer is 37.25 points.

Mean weight of 7 boys = 56 kg.
Total weight of 7 boys = 56 \times 7 kg = 392 kg.
Total weight of 6 boys = (52 + 57 + 55 + 60 + 59 + 55) kg= 338 kg.
Weight of the 7th boy = (total weight of 7 boys) - (total weight of 6 boys) = (392 - 338) kg = 54 kg.
Hence, the weight of the seventh boy is 54 kg.

Total weight of boys in the class = 25 \times 48 = 1200 kgs
Total weight of all students in the class = 45 \times 40 = 1800 kgs
Total weight of the girls in the class = 1800 - 1200 = 600 kgs
Average weight of girls = \frac {600}{15} = 40 kgs

Average of 16 numbers = 8
Thus, total of 16 numbers = 16 \times 8 = 128
When 2 is added to every number then total of 16 numbers increases by 16 \times 2 = 32
Thus, new total of 16 numbers = 128 + 32 = 160
New average of 16 numbers = \frac{160}{16} = 10

Runs scored in the first 10 overs = 10 \times 3.2 = 32
Total runs = 282
Remaining runs to be scored = 282 - 32 = 250
Remaining overs = 40
Run rate needed = \frac{250}{40}=6.25

Average weight of 15 girls = 24 kg
Total weight of 15 girls = 24 \times 15 = 360 kg
Average after including a new girl = 24 + 2 = 26 kg
Total weight of 16 girls = 26 \times 16 = 416 kg
Weight of the new girl = Total weight of 16 girls - Total weight of 15 girls = 416 - 360 = 56 kg.

Hence the required answer is 56 kg.