Question

The average of 11 numbers is 10.8. If the average of the first 6 numbers is 10.4 and the average of the last 6 numbers is 11.5, then the middle number is the sixth.

Correct
option
is 12.6

Average of 11 numbers$ = 10.8$ The sum of 11 numbers $= 10.8 \times 11 = 118.8$ Average of first 6 numbers $= 10.4$ Sum of first 6 numbers $= 10.4 \times 6 = 62.4 $ The sum of the last 6 numbers $= 11.5 \times 6 = 69.0 $ Sixth number = Sum of first 6 numbers + Sum of last 6 numbers - Sum of 11 numbers $= 62.4 + 69.0 - 118.8 = 12.6$

Average of 11 numbers$ = 10.8$ The sum of 11 numbers $= 10.8 \times 11 = 118.8$ Average of first 6 numbers $= 10.4$ Sum of first 6 numbers $= 10.4 \times 6 = 62.4 $ The sum of the last 6 numbers $= 11.5 \times 6 = 69.0 $ Sixth number = Sum of first 6 numbers + Sum of last 6 numbers - Sum of 11 numbers $= 62.4 + 69.0 - 118.8 = 12.6$

Question

The average of 30 results is 20 and the average of the other 20 results is 30. What is the average of all results?

Correct
option
is 24

Sum of 30 results $= 30 \times 20 = 600$ Sum of 20 results $= 30 \times 20 = 600$ Sum of 50 results $= 1200$ Average of 50 results $ = \dfrac{1200}{50}= 24$

Sum of 30 results $= 30 \times 20 = 600$ Sum of 20 results $= 30 \times 20 = 600$ Sum of 50 results $= 1200$ Average of 50 results $ = \dfrac{1200}{50}= 24$

Question

The average of seven consecutive positive integers is 26, the smallest among these integers.

Correct
option
is 23

Let seven consecutive cube integers be $x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6$ is. Average = First Number + Last Number Average $\div$ 2 Average $ = \dfrac {x + x + 6}2 = 26$ $2x + 6 = 52$ $2x = 46$ $x = 23$

Let seven consecutive cube integers be $x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6$ is. Average = First Number + Last Number Average $\div$ 2 Average $ = \dfrac {x + x + 6}2 = 26$ $2x + 6 = 52$ $2x = 46$ $x = 23$

Question

A person walks 2000 meters in 30 minutes, 1500 meters in 40 minutes and 500 meters in 10 minutes, accordingly the average of his total journey will be how many meters per minute

Correct
option
is 50

Total Journeys $= 2000 + 1500 + 500$ $= 4000$ meter Total time taken $= 30 + 40 + 10$ $= 80$ minutes Average travel meter per minute $=\dfrac{ 4000}{80}=50 $

Total Journeys $= 2000 + 1500 + 500$ $= 4000$ meter Total time taken $= 30 + 40 + 10$ $= 80$ minutes Average travel meter per minute $=\dfrac{ 4000}{80}=50 $

Question

The average age of a husband and wife 4 years ago at the time of their marriage was 27 years. Now the average age of a husband, wife and a new born child is 21 years. The current age of the child is

Correct
option
is 1 years

Age of husband and wife 4 years ago $= 27 \times 2 = 54$ years Present age of husband and wife $= 27 + 4 = 31$ years $= 31 \times 2= 62$ years The present total age of husband and wife = 62 years Age of husband and wife and child $= 21 \times 3 = 63$ years So the present age of the child $= 63 - 62 = 1$ year

Age of husband and wife 4 years ago $= 27 \times 2 = 54$ years Present age of husband and wife $= 27 + 4 = 31$ years $= 31 \times 2= 62$ years The present total age of husband and wife = 62 years Age of husband and wife and child $= 21 \times 3 = 63$ years So the present age of the child $= 63 - 62 = 1$ year

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