What is the average of 10, 20, 30, 40 and 50?

30. The sum is 150 and there are 5 values, so the average is 150 5 = 30.

What is the average of the first five multiples of 7?

21. The multiples are 7, 14, 21, 28, 35. Their sum is 105, so the average is 105 5 = 21 (the middle term).

The average age of 30 students is 12 years. When the teacher's age is included, the average rises by 1 year. Find the teacher's age.

43 years. New total = 31 13 = 403; old total = 30 12 = 360. The teacher's age is 403 - 360 = 43 years.

The average of 11 numbers is 50. The average of the first six is 49 and of the last six is 52. What is the sixth number?

56. 6 49 + 6 52 = 294 + 312 = 606 counts the sixth number twice. The true total is 11 50 = 550, so the sixth number is 606 - 550 = 56.

A car covers the first half of a trip at 40 km/h and the second half at 60 km/h. What is its average speed for the whole trip?

48 km/h. For two equal distances at speeds u and v, the average speed is 2uvu+v = 2 40 60100 = 48 km/h.

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Quantitative Aptitude · Averages, Ratios & Percentages

Average — Questions & Answers

Average questions use one core relation — total = average × count — plus the idea of a weighted or combined average. Watch for questions where one value is replaced and the average shifts.

5 solved questions
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Key formulas included

Key formulas

$\text{Average} = \dfrac{\text{sum of values}}{\text{number of values}}$
Combined average of groups: $\dfrac{n_1 \bar{x}_1 + n_2 \bar{x}_2}{n_1 + n_2}$
Average speed for equal distances at $u$ and $v$ : $\dfrac{2uv}{u+v}$

5 solved Average questions

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01
What is the average of 10, 20, 30, 40 and 50?
5 steps · reveal one at a time
1. Step 1: Define Average
  The average (or mean) of a set of numbers is found by summing all the numbers and then dividing by the count of numbers in the set.
2. Step 2: Sum the Values
  First, let's add up all the numbers given in the question: $10 + 20 + 30 + 40 + 50$ . This sum equals $150$ .
3. Step 3: Count Values
  Next, we need to count how many numbers are in the set. We have five numbers: $10, 20, 30, 40,$ and $50$ . So, the count is $5$ .
4. Step 4: Calculate Average
  Now, divide the sum of the numbers by the count of the numbers. That's $150 \div 5 = 30$ .
5. Step 5: The Answer
  So the answer is (A) 30. This is the result of dividing the total sum of 150 by the 5 numbers in the set.
02
What is the average of the first five multiples of 7?
4 steps · reveal one at a time
1. Step 1: List Multiples
  First, we need to find the first five multiples of 7. These are the numbers you get when you multiply 7 by 1, 2, 3, 4, and 5. The multiples are $7$ , $14$ , $21$ , $28$ , and $35$ .
2. Step 2: Sum the Multiples
  Next, we need to find the sum of these five multiples. Add them all together: $7 + 14 + 21 + 28 + 35$ . The total sum is $105$ .
3. Step 3: Calculate Average
  To find the average, we divide the sum by the number of terms. We have 5 multiples, so we divide the sum by 5: $105 \div 5 = 21$ . Notice that 21 is also the middle term.
4. Step 4: The answer
  So the answer is (D) 21. This is the average of the first five multiples of 7, which we found by summing them and dividing by five.
03
The average age of 30 students is 12 years. When the teacher's age is included, the average rises by 1 year. Find the teacher's age.
4 steps · reveal one at a time
1. Step 1: Initial Total Age
  First, calculate the total age of the 30 students. With an average age of 12 years, their combined age is $30 \times 12 = 360$ years.
2. Step 2: New Average and Count
  When the teacher joins, the number of people becomes $30 + 1 = 31$ . The average age increases by 1 year, making the new average $12 + 1 = 13$ years.
3. Step 3: New Total Age
  Next, find the new total age for all 31 individuals (students and teacher). This is calculated as $31 \times 13 = 403$ years.
4. Step 4: The answer
  So the answer is (C) 43 years. The teacher's age is the difference between the new total age and the initial total age: $403 - 360 = 43$ years.
04
The average of 11 numbers is 50. The average of the first six is 49 and of the last six is 52. What is the sixth number?
4 steps · reveal one at a time
1. Step 1: Find total sum
  First, let's find the total sum of all 11 numbers. The average of 11 numbers is 50, so their total sum is $11 \times 50 = 550$ .
2. Step 2: Sum of subgroups
  Now, calculate the sum of the first six numbers and the last six numbers. The sum of the first six is $6 \times 49 = 294$ . The sum of the last six is $6 \times 52 = 312$ .
3. Step 3: Combine sums
  If we add these two sums together, $294 + 312 = 606$ , we have effectively counted the sixth number twice, because it's part of both the first six and the last six numbers.
4. Step 4: The answer
  So the answer is (B) 56. To find the sixth number, subtract the true total sum of all 11 numbers from the combined sum: $606 - 550 = 56$ .
05
A car covers the first half of a trip at 40 km/h and the second half at 60 km/h. What is its average speed for the whole trip?
5 steps · reveal one at a time
1. Step 1: Understand the Problem
  The car travels two equal distances (the first half and the second half of the trip) but at different speeds. We need to find the average speed for the entire journey.
2. Step 2: Recall Average Speed Rule
  For a trip where two equal distances are covered at speeds $u$ and $v$ , the average speed is given by the formula: $\frac{2uv}{u+v}$ . This is a special case of the harmonic mean.
3. Step 3: Apply the Formula
  Substitute the given speeds into the formula. The first speed is $u = 40$ km/h, and the second speed is $v = 60$ km/h. So, we calculate $\frac{2 \times 40 \times 60}{40 + 60}$ .
4. Step 4: Calculate the Result
  First, calculate the numerator: $2 \times 40 \times 60 = 4800$ . Then, calculate the denominator: $40 + 60 = 100$ . Finally, divide: $\frac{4800}{100} = 48$ km/h.
5. Step 5: The answer
  So the answer is (C) 48 km/h. This calculation correctly applies the formula for average speed over two equal distances.

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