Aptitude Solved Problems - Average

Aptitude Solved Problems - Average

Bright Zoom Maths,

Question  : 1

The captain of a cricket team of 11 members is 28 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

Answer: 

25 years

Explanation:

Let the average age of the whole team be x years
Given data, the age of captain of a cricket team = 28 years
If the wicket keeper is 3 years older,
Then, the age of wicket keeper = 28 + 3 = 31
If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team,
Then, new average ⇒ [ 11x - ( 28 + 31 ) ] / 9 = x - 1
[ 11x - 59 ] / 9 = x - 1
( 11x - 59 ) = 9 ( x - 1 )
( 11x - 59 ) = 9x - 9
11x - 9x = 59 - 9
2x = 50
x = 25

∴ The average age of the whole team is 25 years.

Question  : 2

Out of 9 persons, 8 persons spent Rs. 40 each for their meals. The ninth one spent Rs. 30 more than the average expenditure of all the nine. The total money spent by all of them was?

Answer: 

Rs. 393.75

Explanation:

Let the average expenditure be Rs. x
x = [ ( 8 * 40 ) + ( 30 + x ) ] / 9
9 * x = [ ( 8 * 40 ) + ( 30 + x ) ]
9x = 320 + 30 + x
9x = 350 + x
9x - x = 350
8x = 350
x = 350 / 8
x = 43.75
The total money spent by all of them = 9x [ Total persons - 9 ]
= 9 * 43.75
= Rs. 393.75

∴ The total money spent by all of them was Rs. 393.75.

Question  :3

The average salary of all the workers in a workshop is Rs. 9000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?

Answer: 14

Explanation:

Let the total number of workers be x
The total salary of all the workers = 9000 * x
The total salary of 7 workers = 12000 * 7
The no of remaining workers = x - 7
The total salary of ( x - 7 ) remaining workers = 6000 * ( x - 7 )
Then, 9000 * x = 12000 * 7 + 6000 * ( x - 7 )
9000 x = 84000 + 6000 x - 42000
9000 x - 6000 x = 84000 - 42000
3000x = 42000
x = 14

∴ The total number of workers is 14.

Question  :4

The average age of a husband and his wife was 28 years at the time of their marriage. After three years they have a one-year old child. The average age of the family now is?

Answer: 

21 years

Explanation:

Total age of husband and wife at the time of their marriage = 28 * 2
= 56
After three years, the total age of husband and wife

= 56 + 3 + 3
= 56 + 6
= 62
After three years, total age of husband and wife including one-year old child

 = 62 + 1 = 63
The average age of the family at present 

= 63 / 3 = 21

∴ The average age of the family now is 21 years.