Average — Extra Practice — Arithmetic Notes (English Medium)

NoteThis is the Extra Practice set: lots of questions. To learn the methods first, read the main chapter of the same topic (the one without “Extra Practice” in its name), then practise here.

Five children have 12, 15, 18, 20 and 25 marbles. Pool them and share equally, and each gets $\frac{12 + 15 + 18 + 20 + 25}{5} = 18$ . That is their average — one number that stands for the whole group. Every average question in the exam rests on one idea: total = average × count.

∑ Formula

औसत = \frac{सभी का योग}{संख्याओं की गिनती} ⟺ कुल = औसत \times गिनती

The formula to remember

1

Properties of average

Definition · properties · effect of adding and multiplying

Where the average lies, and what happens when something is added to or multiplied into every number.

Finding an average

Sum ÷ count

Four direct properties and finding the missing number.

The average always lies between the smallest and the biggest number. The average of 12, 15, 25 is 17.33 — above 12 and below 25.
If all numbers are equal the average is that number: the average of 7, 7, 7, 7 is 7.
Zero is counted. The average of 4, 8, 0 is $\frac{12}{3} = 4$ , not $\frac{12}{2} = 6$ .
Given the average and the count you know the total: total = average × count — every other formula comes from it.

Example 1 · Basic

A shopkeeper sold ₹4,200, ₹3,850, ₹5,100 and ₹4,650 on four days. What is the average daily sale?

Solution, step by step

1Sum $= 4200 + 3850 + 5100 + 4650 = 17800$ .
2Average $= \frac{17800}{4} = 4450$

Answer ₹4,450

Example 2 · Standard

The average of seven numbers is 24. The first six are 18, 22, 25, 31, 20 and 27. What is the seventh?

Solution, step by step

1Total $= 7 \times 24 = 168$ .
2The six add to $143$ ⟹ the seventh $= 168 - 143 = 25$

Answer 25

BasicTry it yourself first

Find the mean of 14, 22, 18, 26, 30.

BasicTry it yourself first

Find the mean of 7.5, 9.5, 12, 11.

StandardTry it yourself first

Find the mean of 248, 305, 192, 221, 284, 260.

BasicTry it yourself first

The average of 5 numbers is 15. Of them 4 are 12, 16, 14, 18. What is the remaining number?

StandardTry it yourself first

The average of 6 numbers is 38. Of them 5 are 36, 41, 29, 44, 38. What is the remaining number?

AdvancedTry it yourself first

The average of 7 numbers is 80. Of them 6 are 82, 76, 91, 68, 79, 85. What is the remaining number?

When every number changes

The same operation on the average

Whatever you add, subtract, multiply or divide on every number, the average follows.

On every number	On the average
add $a$	$a$ is added
subtract $a$	$a$ is subtracted
multiply by $a$	multiplied by $a$
divide by $a$	divided by $a$

Example 3 · Standard

The average of eight numbers is 15. If every number is multiplied by 4 and then 3 is added, what is the new average?

Solution, step by step

1Multiply by 4: average $15 \times 4 = 60$ .
2Then add 3: $60 + 3 = 63$

Answer 63

BasicTry it yourself first

The average of 10 numbers is 24. If every number is increased by 6, what is the new average?

BasicTry it yourself first

The average of 12 numbers is 35. If every number is decreased by 8, what is the new average?

StandardTry it yourself first

The average of 15 numbers is 18. If each number is multiplied by 5, what is the new average?

StandardTry it yourself first

The average of 9 numbers is 96. If every number is divided by 4, what is the new average?

2

Averages of series

An average without adding

The direct average of natural, even and odd numbers, squares and cubes, and equally spaced series.

Average of the first $n$ numbers

Six formulas

Averages of natural, even, odd numbers, squares, cubes and multiples.

First $n$	Average	Example
natural numbers	$\frac{n + 1}{2}$	1 to 9: $\frac{10}{2} = 5$
even numbers	$n + 1$	2…12 (6 numbers): 7
odd numbers	$n$	1…11 (6 numbers): 6
squares of naturals	$\frac{( n + 1 ) ( 2 n + 1 )}{6}$	$n = 5$ : $\frac{6 \times 11}{6} = 11$
cubes of naturals	$\frac{n ( n + 1 ) ^{2}}{4}$	$n = 4$ : $\frac{4 \times 25}{4} = 25$
multiples of $k$	$\frac{k ( n + 1 )}{2}$	first 8 multiples of 7: $\frac{7 \times 9}{2} = 31.5$

Example 4 · Basic

Find the average of the first 40 natural numbers and of the first 40 even numbers.

Solution, step by step

1Natural: $\frac{40 + 1}{2} = 20.5$ .
2Even: $40 + 1 = 41$ .

Answer $20.5$ and $41$

Example 5 · Standard

Find the average of the cubes of the first 10 natural numbers.

Solution, step by step

1In $\frac{n ( n + 1 ) ^{2}}{4}$ put $n = 10$ : $\frac{10 \times 121}{4}$ .
2 $= 302.5$

Answer 302.5

BasicTry it yourself first

Find the mean of the first 25 natural numbers.

BasicTry it yourself first

Find the mean of the first 15 even numbers.

BasicTry it yourself first

Find the mean of the first 19 odd numbers.

StandardTry it yourself first

Find the mean of the squares of the first 8 natural numbers.

StandardTry it yourself first

Find the mean of the cubes of the first 6 natural numbers.

StandardTry it yourself first

Find the mean of the first 12 multiples of 6.

AdvancedTry it yourself first

Find the mean of the squares of the first 14 natural numbers.

AdvancedTry it yourself first

Find the mean of the cubes of the first 12 natural numbers.

Equally spaced series

Average = (first + last) ÷ 2

When the terms are equally spaced the average is the average of the first and last term.

The series 4, 9, 14, …, 54 is equally spaced (by 5). Average $= \frac{4 + 54}{2} = 29$ — no need to count the middle terms. For consecutive numbers with an odd count the average is the middle number, so “average of 5 consecutive odd numbers is 39” gives 35, 37, 39, 41, 43 at once.

Example 6 · Standard

Find the average of the series 11, 16, 21, …, 96 and the number of terms.

Solution, step by step

1Average $= \frac{11 + 96}{2} = 53.5$ .
2Terms $= \frac{96 - 11}{5} + 1 = 18$ .

Answer $53.5$ and $18$ terms

BasicTry it yourself first

What is the average of the series 3, 7, 11, …, 47?

StandardTry it yourself first

What is the average of the series 14, 20, 26, …, 98?

StandardTry it yourself first

What is the average of the series 7, 16, 25, …, 178?

BasicTry it yourself first

The average of 5 consecutive even / odd numbers is 42. What is the largest?

StandardTry it yourself first

The average of 7 consecutive numbers is 64. What is the largest?

AdvancedTry it yourself first

The average of 9 consecutive even / odd numbers is 110. What is the largest?

3

Weighted averages

The combined average of two or more groups

When the groups differ in size do not average the averages — take total ÷ total count.

Combined average of groups

First the total of each group

Add the group totals and divide by the total count.

∑ Formula

मिला औसत = \frac{n _{1} a _{1} + n _{2} a _{2}}{n _{1} + n _{2}}

For two groups

$n_{1}, n_{2}$: sizes of the groups
$a_{1}, a_{2}$: averages of the groups

CheckThe combined average lies between the two averages and stays closer to the bigger group’s. 40 men averaging 30 and 10 women averaging 20 give 28, not 25.

Example 7 · Standard

In an office 35 men average a salary of ₹24,000 and 15 women ₹32,000. What is the average salary of all?

Solution, step by step

1Total $= 35 \times 24000 + 15 \times 32000 = 840000 + 480000 = 1320000$ .
2Average $= \frac{1320000}{50} = 26400$

Answer ₹26,400

Example 8 · Standard

A shopkeeper bought 12 notebooks at ₹25, 20 pens at ₹8 and 8 registers at ₹40. What is the average price per item?

Solution, step by step

1Total $= 300 + 160 + 320 = 780$ ; items $= 40$ .
2Average $= \frac{780}{40} = 19.5$

Answer ₹19.5

BasicTry it yourself first

In a class 20 boys average 15 and 30 girls average 20. What is the average of the whole class?

BasicTry it yourself first

In a class 40 men average 48 and 10 women average 38. What is the average of the whole class?

StandardTry it yourself first

In a class 36 boys average 62 and 24 girls average 75. What is the average of the whole class?

StandardTry it yourself first

In a class 45 boys average 18.4 and 55 girls average 16.8. What is the average of the whole class?

AdvancedTry it yourself first

In a class 64 students average 71.5 and 36 girl students average 59.5. What is the average of the whole class?

StandardTry it yourself first

A buyer bought 24 books at ₹15 each, 30 pens at ₹6 each, 16 pencils at ₹12 each. Find the mean price of one item.

AdvancedTry it yourself first

A buyer bought 18 books at ₹22 each, 42 pens at ₹7 each, 20 pencils at ₹9 each. Find the mean price of one item.

Removing a part, pass / fail

Subtract the part from the whole

The whole’s average and one part’s average are given — the rest’s average; and pass-fail counts.

Removing a part: if $m$ numbers average $a$ and $n$ of them average $b$ , the other $(m - n)$ average $\frac{ma - nb}{m - n}$ . Pass-fail / officers-staff: call the unknown count $x$ and equate totals (like a mixture).

Example 9 · Standard

The average of 20 numbers is 36. Eight of them average 42. What is the average of the other 12?

Solution, step by step

1Total $= 720$ ; the 8 add to $336$ .
2The other 12 add to $384$ ⟹ average $= 32$ .

Answer 32

Example 10 · Advanced

A class of 66 averages 48 marks. Those who passed average 56 and those who failed 34. How many failed?

Solution, step by step

1Failed $x$ : $34 x + 56 (66 - x) = 66 \times 48$ .
2 $3696 - 22 x = 3168$ ⟹ $22 x = 528$ ⟹ $x = 24$ .

Answer 24

BasicTry it yourself first

The average of 15 numbers is 40. The average of 5 of them is 34. What is the average of the rest?

StandardTry it yourself first

The average of 24 numbers is 52. The average of 9 of them is 44. What is the average of the rest?

StandardTry it yourself first

The average of 30 numbers is 27. The average of 12 of them is 24. What is the average of the rest?

AdvancedTry it yourself first

The average of 45 numbers is 61. The average of 20 of them is 53. What is the average of the rest?

StandardTry it yourself first

A class of 50 students has average marks 52. The average of those who passed is 60 and of those who failed 40. How many failed?

StandardTry it yourself first

A class of 80 students has average marks 54. The average of those who passed is 60 and of those who failed 36. How many failed?

AdvancedTry it yourself first

A class of 120 students has average marks 56. The average of those who passed is 62 and of those who failed 44. How many failed?

4

Changes in an average

Adding · removing · replacing · ages

How the average moves when a number is added, removed or replaced — and recovering that number.

Adding, removing and replacing

Change in total = change in average × count

In all three cases the change in the total does the work.

Situation	Formula
Add one to $n$ numbers (average $a$ ), new average $b$	added $= (n + 1) b - na = n (b - a) + b$
Remove one: average $a \to b$	removed $= na - (n - 1) b = n (a - b) + b$
Replace $x$ by a new one, average changes by $\pm d$	new $= x \pm n d$

Example 11 · Standard

A cricketer’s average over 16 innings is 41. After the 17th innings it becomes 43. How many runs did he score in the 17th?

Solution, step by step

1Runs in 16 innings $= 16 \times 41 = 656$ ; in 17 $= 17 \times 43 = 731$ .
2The 17th innings $= 731 - 656 = 75$

Answer 75

Example 12 · Standard

The average weight of ten people is 62 kg. When the 55 kg person is replaced by a new one the average becomes 63.5 kg. What is the new person’s weight?

Solution, step by step

1Rise in average $= 1.5$ ; rise in total $= 10 \times 1.5 = 15$ kg.
2New weight $= 55 + 15 = 70$ kg

Answer $70$ kg

BasicTry it yourself first

The average of 9 numbers is 34. After one more number is added the average becomes 36. What number was added?

StandardTry it yourself first

The average of 14 numbers is 52. When one number is removed the average becomes 50. What number was removed?

StandardTry it yourself first

The average of 11 numbers is 46. After one more number is added the average becomes 48. What number was added?

AdvancedTry it yourself first

The average of 19 numbers is 58. When one number is removed the average becomes 54. What number was removed?

BasicTry it yourself first

A batsman's average over 9 innings is 36 runs. After the next innings it becomes 41. How many runs did he score in that innings?

StandardTry it yourself first

A batsman's average over 14 innings is 47 runs. After the next innings it becomes 49. How many runs did he score in that innings?

AdvancedTry it yourself first

A batsman's average over 24 innings is 52 runs. After the next innings it becomes 55. How many runs did he score in that innings?

BasicTry it yourself first

The average weight of 8 persons rises by 3 kg when a person of 60 kg is replaced by a new one. What is the new person's weight?

StandardTry it yourself first

The average weight of 12 persons falls by 2 kg when a person of 72 kg is replaced by a new one. What is the new person's weight?

AdvancedTry it yourself first

The average weight of 18 persons rises by 1.5 kg when a person of 66 kg is replaced by a new one. What is the new person's weight?

StandardTry it yourself first

The average of 20 numbers was found to be 38, but one number 26 had been misread as 56. What is the correct average?

AdvancedTry it yourself first

The average of 25 numbers was found to be 42, but one number 91 had been misread as 19. What is the correct average?

Average age

Moving with time

Everyone ages together so the average rises by the same amount; if someone joins or leaves, correct the total.

After $k$ years the average age rises by $k$ (if no one joins or leaves). When a member leaves or joins, work with separate totals: total age = average × members. A new baby adds 0 to the total but one to the count.

Example 13 · Standard

A family of five members averages 28 years. Four years later a baby is born. What is the family’s average age at that moment?

Solution, step by step

1Four years later the five have total age $= 5 \times (28 + 4) = 160$ .
2Baby’s age 0, members 6: average $= \frac{160}{6} = 26 \frac{2}{3}$ years.

Answer $26 \frac{2}{3}$ years

BasicTry it yourself first

A family of 6 members has an average age of 24 years. What will the average age be after 5 years (no one joining or leaving)?

StandardTry it yourself first

A family of 8 members has an average age of 31 years. What will the average age be after 7 years (no one joining or leaving)?

5

Average speed

Total distance ÷ total time

Not the plain mean of speeds — a matter of distance and time.

Three forms of average speed

Equal distances · equal times

Average speed over two or three equal distances and over equal times.

Situation	Average speed
equal distances, speeds $A$ and $B$	$\frac{2 A B}{A + B}$
equal distances, speeds $A, B, C$	$\frac{3 A BC}{A B + BC + C A}$
equal times, speeds $A$ and $B$	$\frac{A + B}{2}$

CheckThe plain mean of speeds is right only when the times are equal. With equal distances you spend longer at the slow speed, so the average speed comes out below the plain mean.

Example 14 · Standard

A bus goes a distance at 48 km/h and returns by the same road at 72 km/h. What is its average speed?

Solution, step by step

1Equal distances: $\frac{2 \times 48 \times 72}{48 + 72}$ .
2 $= \frac{6912}{120} = 57.6$ km/h

Answer $57.6$ km/h

BasicTry it yourself first

A man goes a certain distance at 30 km/h and comes back over the same stretch at 60 km/h. Find his average speed for the whole trip.

StandardTry it yourself first

A man goes a certain distance at 45 km/h and comes back over the same stretch at 90 km/h. Find his average speed for the whole trip.

StandardTry it yourself first

A man goes a certain distance at 36 km/h and comes back over the same stretch at 54 km/h. Find his average speed for the whole trip.

AdvancedTry it yourself first

A man goes a certain distance at 28 km/h and comes back over the same stretch at 42 km/h. Find his average speed for the whole trip.

StandardTry it yourself first

A man covers three equal distances at 20, 30 and 60 km/h respectively. What is his average speed?

AdvancedTry it yourself first

A man covers three equal distances at 12, 18 and 36 km/h respectively. What is his average speed?

AdvancedTry it yourself first

A man covers three equal distances at 40, 60 and 120 km/h respectively. What is his average speed?

6

Traps and fast tricks

Slips · saving time

How marks leak in average questions and how to solve them quickly.

The commonest mistakes

Six traps

The slips that cost marks.

Trap 1Averaging the averages. If 10 people average 40 and 30 average 20 the combined average is 25, not 30. Always weight by the counts.

Trap 2Plain mean of speeds. For equal distances at 30 and 60 km/h the average is 40, not 45.

Trap 3Ignoring a zero or a hidden item. Count every item.

Trap 4Forgetting to reduce the count when something is removed. After removing one, divide by

n - 1

.

Trap 5Changing the count when ages move forward. With no one joining or leaving the count stays and the average just rises by the years.

Trap 6Forgetting to multiply the change by the count. An average that rises by 2 over 8 people means a total rise of 16, not 2.

Fast tricks

Assume · deviation · pairs

Tricks that avoid long addition.

Assumed mean (deviation method): take a nearby number as the average and add each number’s difference from it. For 52, 48, 55, 45, 50 assume 50; the differences $+ 2, - 2, + 5, - 5, 0$ add to 0 ⟹ average 50.
Equally spaced series: (first + last) ÷ 2.
Two groups: the answer stays near the bigger group’s average — use it to cut options.
Average speed, equal distances: always between the two speeds and below the plain mean.
Change formula: new − old = count × change in average.

Example 15 · Standard

Using the deviation method, find the average of 106, 94, 101, 99, 110, 90.

Solution, step by step

1Assume 100. Differences: $+ 6, - 6, + 1, - 1, + 10, - 10$ .
2The differences add to $0$ ⟹ average $= 100$

Answer 100

7

The practice ladder

Basic → standard → advanced

New questions of every type, in three levels.

Level 1 — Basic

Direct rules

One-rule questions.

BasicTry it yourself first

Find the mean of 16, 24, 20, 28, 32, 20.

BasicTry it yourself first

Find the mean of 105, 95, 120, 80.

BasicTry it yourself first

The average of 4 numbers is 26. Of them 3 are 20, 30, 25. What is the remaining number?

BasicTry it yourself first

The average of 5 numbers is 20. Of them 4 are 15, 18, 21, 24. What is the remaining number?

BasicTry it yourself first

The average of 7 numbers is 30. If every number is increased by 9, what is the new average?

BasicTry it yourself first

The average of 14 numbers is 22. If each number is multiplied by 3, what is the new average?

BasicTry it yourself first

Find the mean of the first 31 natural numbers.

BasicTry it yourself first

Find the mean of the first 20 even numbers.

BasicTry it yourself first

Find the mean of the first 13 odd numbers.

BasicTry it yourself first

What is the average of the series 5, 10, 15, …, 50?

BasicTry it yourself first

The average of 3 consecutive numbers is 41. What is the largest?

BasicTry it yourself first

In a class 10 boys average 30 and 10 girls average 50. What is the average of the whole class?

BasicTry it yourself first

In a class 30 boys average 10 and 20 girls average 15. What is the average of the whole class?

BasicTry it yourself first

The average of 10 numbers is 50. The average of 4 of them is 45. What is the average of the rest?

BasicTry it yourself first

The average of 7 numbers is 25. After one more number is added the average becomes 27. What number was added?

BasicTry it yourself first

The average of 6 numbers is 40. When one number is removed the average becomes 38. What number was removed?

BasicTry it yourself first

The average weight of 5 persons rises by 4 kg when a person of 50 kg is replaced by a new one. What is the new person's weight?

BasicTry it yourself first

A batsman's average over 5 innings is 30 runs. After the next innings it becomes 35. How many runs did he score in that innings?

BasicTry it yourself first

A man goes a certain distance at 40 km/h and comes back over the same stretch at 60 km/h. Find his average speed for the whole trip.

BasicTry it yourself first

A family of 5 members has an average age of 20 years. What will the average age be after 3 years (no one joining or leaving)?

Level 2 — Standard

Two ideas combined

Exam-level questions.

StandardTry it yourself first

Find the mean of 1,250, 1,480, 1,315, 1,690, 1,425, 1,560, 1,380.

StandardTry it yourself first

Find the mean of 3.6, 4.8, 5.2, 2.9, 4.5.

StandardTry it yourself first

The average of 6 numbers is 55. Of them 5 are 48, 52, 61, 45, 57. What is the remaining number?

StandardTry it yourself first

The average of 5 numbers is 26. Of them 4 are 23.5, 27.5, 30, 21. What is the remaining number?

StandardTry it yourself first

The average of 16 numbers is 45. If every number is decreased by 12, what is the new average?

StandardTry it yourself first

The average of 20 numbers is 84. If every number is divided by 6, what is the new average?

StandardTry it yourself first

Find the mean of the squares of the first 9 natural numbers.

StandardTry it yourself first

Find the mean of the cubes of the first 8 natural numbers.

StandardTry it yourself first

Find the mean of the first 15 multiples of 4.

StandardTry it yourself first

What is the average of the series 12, 19, 26, …, 131?

StandardTry it yourself first

The average of 9 consecutive even / odd numbers is 63. What is the largest?

StandardTry it yourself first

The average of 11 consecutive numbers is 81. What is the largest?

StandardTry it yourself first

In a class 48 boys average 56 and 72 girls average 64. What is the average of the whole class?

StandardTry it yourself first

In a class 25 boys average 41.2 and 15 girls average 36.4. What is the average of the whole class?

StandardTry it yourself first

In a class 60 apples average 33 and 40 oranges average 48. What is the average of the whole class?

StandardTry it yourself first

A buyer bought 15 books at ₹20 each, 25 pens at ₹12 each, 10 pencils at ₹30 each. Find the mean price of one item.

StandardTry it yourself first

The average of 36 numbers is 48. The average of 15 of them is 52. What is the average of the rest?

StandardTry it yourself first

The average of 28 numbers is 63. The average of 10 of them is 70. What is the average of the rest?

StandardTry it yourself first

A class of 85 students has average marks 51. The average of those who passed is 58 and of those who failed 41. How many failed?

StandardTry it yourself first

A class of 100 students has average marks 57. The average of those who passed is 65 and of those who failed 45. How many failed?

StandardTry it yourself first

The average of 12 numbers is 38. After one more number is added the average becomes 40. What number was added?

StandardTry it yourself first

The average of 16 numbers is 46. When one number is removed the average becomes 44. What number was removed?

StandardTry it yourself first

The average weight of 9 persons rises by 5 kg when a person of 64 kg is replaced by a new one. What is the new person's weight?

StandardTry it yourself first

The average weight of 15 persons falls by 3 kg when a person of 80 kg is replaced by a new one. What is the new person's weight?

StandardTry it yourself first

A batsman's average over 11 innings is 38 runs. After the next innings it becomes 40. How many runs did he score in that innings?

StandardTry it yourself first

A batsman's average over 19 innings is 44 runs. After the next innings it becomes 46. How many runs did he score in that innings?

StandardTry it yourself first

The average of 30 numbers was found to be 52, but one number 47 had been misread as 74. What is the correct average?

StandardTry it yourself first

A man goes a certain distance at 24 km/h and comes back over the same stretch at 36 km/h. Find his average speed for the whole trip.

StandardTry it yourself first

A man goes a certain distance at 50 km/h and comes back over the same stretch at 75 km/h. Find his average speed for the whole trip.

StandardTry it yourself first

A man covers three equal distances at 30, 45 and 90 km/h respectively. What is his average speed?

StandardTry it yourself first

A family of 7 members has an average age of 33 years. What will the average age be after 9 years (no one joining or leaving)?

Level 3 — Advanced

Many steps and clever thinking

Questions at the hard end of competitive exams.

AdvancedTry it yourself first

Find the mean of 4.75, 5.25, 6.5, 3.25, 7.75, 4.5, 5.5, 6.25.

AdvancedTry it yourself first

The average of 8 numbers is 80. Of them 7 are 72, 85, 91, 68, 77, 83, 79. What is the remaining number?

AdvancedTry it yourself first

The average of 25 numbers is 18.4. If each number is multiplied by 5, what is the new average?

AdvancedTry it yourself first

The average of 18 numbers is 56.5. If every number is decreased by 7.5, what is the new average?

AdvancedTry it yourself first

Find the mean of the squares of the first 17 natural numbers.

AdvancedTry it yourself first

Find the mean of the cubes of the first 15 natural numbers.

AdvancedTry it yourself first

Find the mean of the first 24 multiples of 9.

AdvancedTry it yourself first

What is the average of the series 23, 36, 49, …, 413?

AdvancedTry it yourself first

The average of 13 consecutive even / odd numbers is 156. What is the largest?

AdvancedTry it yourself first

In a class 85 boys average 47.6 and 65 girls average 58.4. What is the average of the whole class?

AdvancedTry it yourself first

A buyer bought 40 books at ₹12 each, 25 pens at ₹18 each, 35 pencils at ₹16 each. Find the mean price of one item.

AdvancedTry it yourself first

The average of 55 numbers is 62. The average of 23 of them is 68. What is the average of the rest?

AdvancedTry it yourself first

The average of 48 numbers is 71.5. The average of 18 of them is 58. What is the average of the rest?

AdvancedTry it yourself first

A class of 150 students has average marks 58. The average of those who passed is 64 and of those who failed 46. How many failed?

AdvancedTry it yourself first

A class of 126 students has average marks 49. The average of those who passed is 55 and of those who failed 37. How many failed?

AdvancedTry it yourself first

The average of 24 numbers is 57. After one more number is added the average becomes 58.5. What number was added?

AdvancedTry it yourself first

The average of 31 numbers is 66. When one number is removed the average becomes 64. What number was removed?

AdvancedTry it yourself first

The average weight of 20 persons rises by 2.5 kg when a person of 58 kg is replaced by a new one. What is the new person's weight?

AdvancedTry it yourself first

The average weight of 24 persons falls by 1.5 kg when a person of 92 kg is replaced by a new one. What is the new person's weight?

AdvancedTry it yourself first

A batsman's average over 29 innings is 51 runs. After the next innings it becomes 53. How many runs did he score in that innings?

AdvancedTry it yourself first

A batsman's average over 39 innings is 46 runs. After the next innings it becomes 49. How many runs did he score in that innings?

AdvancedTry it yourself first

The average of 40 numbers was found to be 61, but one number 98 had been misread as 28. What is the correct average?

AdvancedTry it yourself first

A man goes a certain distance at 56 km/h and comes back over the same stretch at 84 km/h. Find his average speed for the whole trip.

AdvancedTry it yourself first

A man covers three equal distances at 24, 36 and 72 km/h respectively. What is his average speed?

AdvancedTry it yourself first

A man covers three equal distances at 48, 72 and 144 km/h respectively. What is his average speed?

AdvancedTry it yourself first

A family of 12 members has an average age of 41 years. What will the average age be after 16 years (no one joining or leaving)?

AdvancedTry it yourself first

A batch of 20 students has an average weight of 58 kg. Six new students with an average weight of 64 kg join. What is the average weight of the 26 students now?

8

Revision — formula cards

Flip each card and test yourself

Read the front, think, then flip.