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## [Smart Math] Averages Problem 15

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

Nine men went to a restaurant. Eight of them spent $6 each for their meals and the ninth man spent$4 more than the average expenditure of all nine men. What is the average expenditure?

1. $5.00 2.$5.50
3. $6.50 4.$7.50
5. \$10.00
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## [Smart Math] Averages Problem 14

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

The average age of a couple married four years ago was 25 years then. The average age of the family consisting of husband, wife and a child now is 20 years. What is the child’s present age?

1. less than 1 year old
2. 1 year
3. 2 years
4. 3 years
5. 4 years

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## [Smart Math] Averages Problem 13

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

The average age of 20 boys of a class is 12 years. Ten new boys are admitted and the average age increases by a year. The average age of the new boys is ________ years?

1. 13
2. 14
3. 15
4. 16
5. 18
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## [Smart Math] Averages Problem 12

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

The average weight of 10 sacks of wheat is decreased by 1 lb when 2 of them 26 and 30 lbs are replaced by 2 rice sacks. What was the average weight of the two rice sacks?

1. 21 lbs
2. 22 lbs
3. 23 lbs
4. 24 lbs
5. 25 lbs
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## [Smart Math] Averages Problem 11

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

The average temperature for the first 9 days was 20 ${}^\circ$C and that of the first 5 was 25 ${}^\circ$C and that for the last 5 days was 15 ${}^\circ$C. What was the temperature on the fifth day?

1. 25 ${}^\circ$C
2. 20 ${}^\circ$C
3. 30 ${}^\circ$C
4. 15 ${}^\circ$C
5. 27 ${}^\circ$C
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## [Smart Math] Averages Problem 10

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

The average weight of a sac of wheat in a truck is reduced by 0.2 lbs from 50 lbs when 5 new sacs, each weighing 47.4 lbs on an average, are loaded. How many sacs did the truck originally carried?

1. 60
2. 62
3. 64
4. 66
5. 68
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## [Smart Math] Averages Problem 9

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

The average age of Allen and Beth is 40 years. If Chris were to replace Allen, the average would be 38 years and if he were to replace Beth, the average would be 42 years. What are the ages of Allen, Beth and Chris respectively?

1. 44, 44, 36
2. 36, 44, 40
3. 44, 40, 36
4. 36, 40, 44
5. 44, 36, 40
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## [Smart Math] Averages Problem 8

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

The average attendance in a class for the first four days of the week is 32 and for the first 5 days is 33. How many students were present on the fifth day?

1. 36
2. 37
3. 38
4. 39
5. 40
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## [Smart Math] Averages Problem 7

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

The average age of 25 students of a class is 10 years. When a new student is admitted, the average age becomes 10.1 years. What is the age of the new student?

1. 10.1 years
2. 10.6 years
3. 11.6 years
4. 12.0 years
5. 12.6 years
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## [Smart Math] Averages Problem 6

Here’s and example of a SMART MATH problem for AVERAGES. ### Problem

The captain of a certain team of 11 players is 25 years old and the vice captain is 3 years older. If the ages of these two players are excluded, the average age of the remaining players is 1 year less then the average age of the whole team. What is the average age of the whole team?

1. 21.5 years
2. 22 years
3. 22.5 years
4. 23 years
5. 25 years

The Usual Method

Total age of captain and vice captain = 25 + (25 + 3) = 53 years.

Let the average age of all players be ‘x’ years.

Hence, total age of 11 players = 11x years $11x-53=9(x-1)$ $\therefore 11x-53=9x-9$ $\therefore 2x=44$ $\therefore x=22$years

Hence, average age of the whole team = 22 years

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

53 – 9 = 44 years will be the age of 2 players of the team. Hence, average age of the team = $\frac{44}{2}=22$years