Q: Three numbers are such that when the average of any two is added to the third, the results are 200, 180, and 160. What is the average of the three numbers?

90. If the numbers are x, y, z, then $\frac{x+y}{2}+z=200$, $\frac{y+z}{2}+x=180$, and $\frac{z+x}{2}+y=160$. Adding all three gives $2(x+y+z)=540$, so $x+y+z=270$. Therefore, the average is $270/3=90$.

Q: The average weight of 30 students in a class is 50 kg. If the weight of the teacher is added, the average rises to 51 kg. What is the teacher's weight?

81 kg. The total weight of 30 students is $30\times 50=1500$ kg. After adding the teacher, average becomes 51 kg for 31 people, so total weight = $31\times 51=1581$ kg. Teacher's weight = $1581-1500=81$ kg.

Q: A group of 6 friends went to a cafe. If 5 of them paid Rs. 300 each and the sixth paid Rs. $y$, the average bill per person was Rs. 320. What is the value of $y$?

Rs. 420. The total bill is $6 \times 320 = 1920$. Five friends paid $5 \times 300 = 1500$, so the sixth paid $1920 - 1500 = 420$.

Question 1

Two farmers, X and Y, hire a field. X keeps 18 oxen there for 5 months and 20 goats for 3 months. Y keeps 24 goats for 7 months and 30 sheep for 6 months. If 2 oxen eat as much as 5 goats, and 3 goats eat as much as 4 sheep, what fraction of the total rent should X pay?

Accepted Answer

95/196. Rent is divided in proportion to the total consumption of each farmer's animals. Using the given relations, express oxen and sheep in terms of goats, then compute the total goat-equivalent months for X and Y. The fraction paid by X is his share of the total consumption.

Question 2

Three batches of students have average ages 17, 19, and 23 years respectively. If their numbers are in the ratio 3:4:6, what is the overall average age of all the students?

Accepted Answer

20.38. The overall average is the weighted average of the three batch averages. Using weights 3, 4, and 6 gives (173 + 194 + 236)/(3+4+6). This equals 265/13 20.38.

Question 3

The average of 13 numbers is 75. If the average of the first six numbers is 69 and the average of the last six numbers is 80, what is the 7th number?

Accepted Answer

81. The sum of all 13 numbers is 1375 = 975. The sum of the first six is 669 = 414 and the sum of the last six is 680 = 480. Since these two groups cover 12 numbers and together include the 7th number once each, the 7th number is 414 + 480 - 975 = 81.

Question 4

Three numbers are such that when the average of any two is added to the third, the results are 200, 180, and 160. What is the average of the three numbers?

Accepted Answer

90. If the numbers are x, y, z, then $\frac{x+y}{2}+z=200$, $\frac{y+z}{2}+x=180$, and $\frac{z+x}{2}+y=160$. Adding all three gives $2(x+y+z)=540$, so $x+y+z=270$. Therefore, the average is $270/3=90$.

Question 5

The average of 11 numbers is 48. When one number is removed, the average becomes 45. What number was removed?

Accepted Answer

78. Sum of 11 numbers = 11×48 = 528. After removing one number, sum of remaining 10 numbers = 10×45 = 450. The removed number is 528 - 450 = 78.

Question 6

The average height of 50 students was calculated as 170 cm. Later, it was found that the height of one student was misread as 178 cm instead of 158 cm. Find the correct average height.

Accepted Answer

169.6 cm. The गलत total based on the wrong average is 50 × 170 = 8500 cm. Since 178 cm was read instead of 158 cm, the total was overstated by 20 cm, so the correct total is 8480 cm. Dividing by 50 gives the correct average as 169.6 cm.

Question 7

The average weight of 25 workers is 64 kg. If the manager is excluded, the average weight decreases by 1 kg. What is the weight of the manager?

Accepted Answer

88 kg. The total weight of 25 workers is 25 × 64 = 1600 kg. After excluding the manager, the average becomes 63 kg for 24 workers, so their total is 24 × 63 = 1512 kg. Therefore, the manager's weight is 1600 - 1512 = 88 kg.

Question 8

The average weight of 30 students in a class is 50 kg. If the weight of the teacher is added, the average rises to 51 kg. What is the teacher's weight?

Accepted Answer

81 kg. The total weight of 30 students is $30\times 50=1500$ kg. After adding the teacher, average becomes 51 kg for 31 people, so total weight = $31\times 51=1581$ kg. Teacher's weight = $1581-1500=81$ kg.

Question 9

A trader bought four varieties of coffee whose weights are in the ratio $1:2:3:4$. Their respective prices per kg are Rs. 100, Rs. 120, Rs. 150, and Rs. 180. What is the average cost per kg of the mixture?

Accepted Answer

Rs. 151. The average cost per kg of a mixture is the weighted average of the component prices. Using weights $1,2,3,4$, total cost $=100\cdot1+120\cdot2+150\cdot3+180\cdot4=1510$ and total weight $=1+2+3+4=10$. So the average cost per kg is $1510/10=Rs.\ 151$.

Question 10

A group of 6 friends went to a cafe. If 5 of them paid Rs. 300 each and the sixth paid Rs. $y$, the average bill per person was Rs. 320. What is the value of $y$?

Accepted Answer

Rs. 420. The total bill is $6 \times 320 = 1920$. Five friends paid $5 \times 300 = 1500$, so the sixth paid $1920 - 1500 = 420$.

Question 11

A group of 6 students went on a trip and spent Rs. 1200 in total. If one of them spent Rs. 300 while the rest spent equally, what was the average spending of the other 5 students?

Accepted Answer

Rs. 180. Total spending is Rs. 1200. One student spent Rs. 300, so the remaining 5 students spent Rs. 900 together. Their average spending is 900 ÷ 5 = Rs. 180.

Question 12

A student took 7 tests and had an average of 72. If his average after 8 tests increased to 73, what was his score on the 8th test?

Accepted Answer

80. The total for 7 tests is 7 × 72 = 504. The total for 8 tests is 8 × 73 = 584. So the 8th test score is 584 - 504 = 80.

Question 13

A cricketer has played 8 innings with an average score of 40. In the next inning, he scores 80. What will be the new average?

Accepted Answer

44.44. Total runs in 8 innings = $8 \times 40 = 320$. After scoring 80 more, total runs become 400 in 9 innings. New average = $400/9 = 44.44$ (approx.).

Question 14

In a company, the average salary of 5 junior employees is Rs. 30,000, and that of 4 senior employees is Rs. 60,000. What is the combined average salary?

Accepted Answer

Rs. 43,333.33. The total salary of 5 juniors is $5 \times 30000 = 150000$, and of 4 seniors is $4 \times 60000 = 240000$. Total salary = $390000$ for 9 employees, so the combined average is $390000/9 = 43333.33$.

Question 15

The average of 8 numbers is 56. If two of them are removed and the new average becomes 54, what is the average of the two removed numbers?

Accepted Answer

62. The sum of 8 numbers is 8 × 56 = 448. After removing 2 numbers, the sum of the remaining 6 numbers is 6 × 54 = 324, so the removed numbers sum to 124 and their average is 62.

Question 16

A class of 60 students has an average score of 75. If 5 new students are added and the class average increases by 1, what is the average score of the 5 new students?

Accepted Answer

88. Initial total score = 60 × 75 = 4500. New average = 76 for 65 students, so new total = 65 × 76 = 4940. Therefore, the 5 new students scored 4940 − 4500 = 440, giving an average of 88.

Question 17

An investor tracks 5 stocks. Four of them have an average return of 8%. If the overall average return is 9%, what was the return on the fifth stock?

Accepted Answer

13%. The total return of 5 stocks is 5 × 9% = 45%. The first 4 stocks contribute 4 × 8% = 32%. So the fifth stock's return is 45% - 32% = 13%.

Question 18

The average age of 10 students in a class increases by 1 year when a 30-year-old teacher joins them. What was the original average age of the students?

Accepted Answer

19. If the average of 10 students increases by 1 year, the total age of the group of 10 students increases by 10 when the teacher is included in the new average setup. Let the original average be $x$; then the new average becomes $x+1$. Using the teacher's age of 30, the original average works out to 19 years.

SSC CGL (Prelims) General: Average questions with solutions

Questions