Average problems
- 1. In a mens hostel, there were 95 students. To accommodate 30 more students the average is decreased by rupees 5. But total expenditure increased by Rs.500. Find the total expenditure of the hostel now ?
Options- A. Rs. 4680
- B. Rs. 4420
- C. Rs. 4960
- D. Rs. 5480 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: Rs. 4680
Explanation:
Let the expenditure on the 95 students be 'x'
Then,
95x + 500 = 120(x ? 5)
95x + 500 = 120x - 600
120x - 95x = 1100
25x = 1100
=> x = 44
Therefore, total expenditure of the hostel becomes
95 x 44 + 500 = 4680.
- 2. The mean of 100 observations is 40. It is found that an observation 84 was misread as 48. Then the correct mean is ?
Options- A. 40.36
- B. 41.24
- C. 41.92
- D. 42.05 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 40.36
Explanation:
Given,
mean of 100 observations is 40
=> Total of 100 observations = 40 x 100 = 4000
84 is misread as 48
=> Difference = 84 - 48 = 36
=> Now, new total of 100 observations = 4000 + 36 = 4036
Correct Mean = 4036/100 = 40.36
- 3. Without any stoppage, a person travels a certain distance at an average speed of 42 km/h, and with stoppages he covers the same distance at an average speed of 28 km/h. How many minutes per hour does he stop?
Options- A. 15 minutes
- B. 20 minutes
- C. 18 minutes
- D. 22 minutes Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 20 minutes
Explanation:
Let the total distance to be covered is 84 kms.
Time taken to cover the distance without stoppage = 84/42 hrs = 2 hrs
Time taken to cover the distance with stoppage = 84/28 = 3 hrs.
Thus, he takes 60 minutes to cover the same distance with stoppage.
Therefore, in 1 hour he stops for 20 minutes.
- 4. The average age of 7 boys is increased by 1 year when one of tem whose age is replaced by a girl. What is the age of the girl ?
Options- A. 33 yrs
- B. 27 yrs
- C. 21 yrs
- D. 29 yrs Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 29 yrs
Explanation:
Let the avg age of 7 boys be 'p' years
Let the age of the girl be 'q' years
From given data,
The age of 7 boys = 7p years
Now the new average = (p + 1) when 22 yrs is replaced by q
Now the age of all 7 will become = 7(p + 1) yrs
Hence, 7p - 22 + q = 7(p + 1) yrs
7p - 22 + q = 7p + 7
q = 22 + 7 = 29
Therefore, the age of girl = q = 29 years.
- 5. The ratio of speeds of a car, a train and a bus is 5:9:4. The average speed of the car, the bus and the train is 72 km/hr together. What is the average speed of the car and the train together ?
Options- A. 84 km/hr
- B. 96 km/hr
- C. 72 km/hr
- D. 60 km/hr Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, GRE
Correct Answer: 84 km/hr
Explanation:
Let the speeds of the car, train and bus be 5x, 9x and 4x km/hr respectively.
Average speed = 5x + 9x + 4x/3 = 18x /3 = 6x km/hr.
Also, 6x = 72 => x = 12 km/hr
Therefore, the average speed of the car and train together is =
= 7x = 7 x 12 = 84 km/hr.
- 6. Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, what will be the sum of the highest number and the lowest number?
Options- A. 120
- B. 160
- C. 80
- D. 60 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 120
Explanation:
Let the three numbers be x, y, z.
From the gien data,
x = 2y ....(1)
x = z/2 => z = 2(2y) = 4y .....(From 1) ...........(2)
Given average of three numbers = 56
Then,
Now,
x = 2y => x = 2 x 24 = 48
z = 4y = 4 x 24 = 96
Now, the highest number is z = 96 & smallest number is y = 24
Hence, required sum of highest number and smallest number
= z + y
= 96 + 24
= 120.
- 7. After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. The difference between the ages of the replaced and the new members?
Options- A. 16 years
- B. 15 years
- C. 14 years
- D. 13 years Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 15 years
Explanation:
Let avg ages of 5 members at present is G
And age of new member is m and an older is n
Required = (5G + m - n)/5 = G - 3
m - n = 15 years
- 8. In a mixture of three varities of oils , the ratio of their weight is 4 : 5 : 8. If 5 kg of oils of the first variety, 10 kg of the second variety and some quantity of oils of the third variety are added to the mixture, the ratio of the weights of three varieties of oils becomes as 5 : 7 : 9 in the final mixture, find the quantity of third variety of oil was ?
Options- A. 15 kg
- B. 25 kg
- C. 35 kg
- D. 45 kg Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 45 kg
Explanation:
Let the ratio of initial quantity of oils be 'x' => 4x, 5x & 8x.
Let k be the quantity of third variety of oil in the final mixture.
Let the ratio of initial quantity of oils be 'y'
From given details,
4x + 5 = 5y ..... (1)
5x + 10 = 7y .....(2)
8x + k = 9y ......(3)
By solving (1) & (2), we get
x = 5 & y = 5
From (3) => k = 5
Therefore, quantity of third variety of oil was 9y = 9(5) = 45kg.
- 9. What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58 ?
Options- A. Rs. 3748
- B. Rs. 3847
- C. Rs. 3944
- D. Rs. 3154 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: Rs. 3944
Explanation:
Let the side of the square plot be 'a' ft.
Given area of the plot (a x a) = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 x 58 = Rs. 3944.
- 10. It costs Rs. p each to send the first thousand messsages and Rs. q to send each subsequent one . If r is greater than 1,000, how many Rupees will it cost to send r messages ?
Options- A. 1000 (r - p) + pq
- B. 1000 p + qr
- C. 1000 (r - q) + pr
- D. 1000(p - q) + qr Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 1000(p - q) + qr
Explanation:
We need to find the total cost to send r messsages, r > 1000.
The first 1000 messsages will cost Rs.p each (Or)
The total cost of first 1000 messsages = Rs.1000p
The remaining (r - 1000) messsages will cost Rs.q each (Or)
The cost of the (r - 1000) = Rs.(r - 1000)y
Therefore, total cost = 1000p + rq - 1000q
= 1000(p - q) + qr
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