## Problems on Averages Set - 3

1. The average price of 80 computers in an electronic shop is Rs30,000. If the highest and lowest price computers are sold out then the average price of the remaining 78 computers is Rs.29,500. The cost of the highest price computer is Rs.80,000. The cost of lowest price computer is
(a)Rs.19,000
(b) Rs.20,000
(c)Rs.29,000
(d) Can‟t be determined
(e) None of these
2. The average salary of all the 60 employees in an office is Rs.12,000 per month. If the number of executive is twice the number of non-executive employees, then the average salary of all the non-executive employees
(a) Rs.9000
(b) Rs.8000
(c) Rs.6000
(d) Can‟t be determined
(e) None of these
3. Mr. Sharma travels by car and covers 25% of his journey with a speed of 10 km/h, 45% of his journey with a speed of 5 km/h and remaining 30% of his journey with a speed of 15 km/h. what will be the average speed of Mr. Sharma for the whole journey?
(a) 7.40km/h
(b) 7.45 km/h
(c) 8.0km/h
(d) 6.5 km/h
(e) 8.5 km/h
4. Gopal went to the Hospital at the speed of 60 km/hr while returning for his home he covered the half of the distance at the speed of 10 km/hr, but suddenly he realized that he was getting late so he increased the speed and reached the home by covering rest half of the distance at the speed of 30km/hr. The average speed of the Gopal in the whole length of journey is:
(a) 5.67 km/hr
(b) 24 km/hr
(c) 22.88 km/hr
(d) 5.45 km/hr
(e) 12.86 km/hr
5. In a class, there are 75 students and their average mark in the annual examination is 35. If the average marks of passed student‟s is55 and average marks of failed students is 30, then find out the number students who failed
(a) 60
(b) 65
(c) 70
(d) 75
(e) None of these
6. The average runs scored by a cricketer in 42 innings, is 30. The difference between his maximum and minimum scores in an innings is 100. If these two innings are not taken into consideration, then the average score of remaining 40 innings is 28. Calculate the maximum runs scored by him in an innings?
(a) 125
(b) 120
(c) 110
(d) 100
(e) 105
7. On an average 300 people watch the movie in Sahu Cinema hall on Monday, Tuesday and Wednesday and the average number of visitors on Thursday and Friday is 250. If the average number of visitors per day in the week be 400, then the average number of people who watch the movie in weekends (i.e., on Saturday and Sunday) is:
(a) 500
(b) 600
(c) 700
(d) 800
(e) 850
8. The average weight of 5 men is decreased by 3 kg when one of them weighing 150 kg is replaced by another person. This new person is again replaced by another person whose weight is 30 kg lower than the person he replaced. What is the overall change in the average due to this dual change?
(a) 6 kg
(b) 9 kg
(c) 12 kg
(d) 15kg
(e) 18 kg
9. There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?
(a) 420
(b) 400
(c) 480
(d) 460
(e) 450
10. The average price of 10 books is Rs.12 while the average price of 8 of these books is Rs.11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?
(a) Rs. 5, Rs.8
(b) Rs. 8, Rs. 12.8
(c) Rs. 10, Rs. 16
(d) Rs. 12, Rs. 19.2
(e) None of these
Solutions:  4. Let the distance = x
Average speed = total distance/total time
= (x + x)/[(x/60) + (x/2 × 10) + (x/2 × 30)] = 2x/[(x + 3x + x)/60] = 24kmph
5. 6. Let the minimum score =x
Maximum score = x+100
𝑥+ 𝑥+100 = 30×42−40×28
=> 2𝑥+100=1260−1120=140
=> 2𝑥=40 => 𝑥=20
Hence, the maximum score= x+100 =20+100=120
7. Monday + Tuesday + Wednesday= 300×3=900
Thursday + Friday =250×2=500
Monday to Sunday =400×7=2800
Required average =1/2 [2800− (900+500)] =700
8. The weight of 2nd person is (150−3×5)=135𝑘𝑔
The weight of the 3rd person is =135−30=105 𝑘𝑔
Thus the change of the 5 person =150−105=45 𝑘𝑔
Hence overall change =45/5𝑘𝑔=9 𝑘𝑔
9. Let Average expenditure per head be = x
So, (35+7) (𝑥−1) −35𝑥=42
=> 42 (𝑥−1) −35𝑥=42 => 𝑥=12
Original expenditure of mess =12×35=420
10. Total cost of 10 books = Rs. 120 --->(1)
Total cost of 8 books = Rs. 94 -----> (2)
Subtracting (1) & (2), We get,
The cost of 2 books = Rs. 26
Let the price of each book be x and y,
𝑥+𝑦=26 ------> (3)
1 book is 60% more than other price => 160y/100 + y = 26 => y = 10
Substitute in (3) 𝑥+10=26 => 𝑥=16
The price of each of these two books = Rs.10 & Rs.16