Average problems
- 1. 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
- 2. Three maths classes: A, B and C take an algebra test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. What is the average score of classes A, B, C ?
Options- A. 81
- B. 78
- C. 80.5
- D. 81.5 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 81.5
Explanation:
Let the number of students in classes A, B and C be P, Q and R respectively.
Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R.
Also given that,
(83P + 76Q) / (P + Q) = 79
=>4P = 3Q.
(76Q + 85R)/(Q + R) = 81
=>4R = 5Q,
=>Q = 4P/3 and R = 5P/3
Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R) = 978/12 = 81.5
- 3. The average of marks in 3 subjects is 224. The first subject marks is twice the second and the second subject marks is twice the third. Find the second subject marks ?
Options- A. 384
- B. 96
- C. 192
- D. 206 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 192
Explanation:
Let the third subject marks be 'x'
=> Second subject marks = 2x
=> Third subject marks = 4x
Given avg = 224
x + 2x + 4x = 224 x 3
=> 7x = 224 x 3
=> x = 96
Hence, Second subject marks = 2x = 2 x 96 = 192.
- 4. How many window coverings are necessary to span 50 windows, if each window covering is 15 windows long?
Options- A. 4
- B. 15
- C. 3
- D. 50 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer
Correct Answer: 4
Explanation:
Given that,
Number of windows = 50
Each window covering covers 15 windows
=> 50 windows requires 50/15 window coverings
= 50/15 = 3.333
Hence, more than 3 window coverings are required. In the options 4 is more than 3.
Hence, 4 window coverings are required to cover 50 windows of each covering covers 15 windows.
- 5. There are 44 students in a hostel, due to the administration, 15 new students has joined. The expense of the mess increase by Rs. 33 per day. While the average expenditure per head diminished by Rs. 3, what was the original expenditure of the mess ?
Options- A. Rs. 404
- B. Rs. 514
- C. Rs. 340
- D. Rs. 616 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: Rs. 616
Explanation:
Let the average expenditure per head be Rs. p
Now, the expenditure of the mess for old students is Rs. 44p
After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3
Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33
Therefore, 59(p-3) = 44p + 33
59p - 177 = 44p + 33
15p = 210
=> p = 14
Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.
- 6. On a school?s Annual day sweets were to be equally distributed amongst 112 children. But on that particular day, 32 children were absent. Thus the remaining children got 6 extra sweets. How many sweets was each child originally supposed to get ?
Options- A. 14
- B. 16
- C. 12
- D. 15 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 15
Explanation:
Let 'K' be the total number of sweets.
Given total number of students = 112
If sweets are distributed among 112 children,
Let number of sweets each student gets = 'L'
=> K/112 = L ....(1)
But on that day students absent = 32 => remaining = 112 - 32 = 80
Then, each student gets '6' sweets extra.
=> K/80 = L + 6 ....(2)
from (1) K = 112L substitute in (2), we get
112L = 80L + 480
32L = 480
L = 15
Therefore, 15 sweets were each student originally supposed to get.
- 7. The average monthly salary of 24 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 400. What is the manager's monthly salary ?
Options- A. Rs. 8840
- B. Rs. 11,500
- C. Rs. 12,800
- D. Rs. 9450 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: Rs. 11,500
Explanation:
Manager's monthly salary
= Rs. (1900 x 25 - 1500 x 24) = Rs. 11,500
- 8. Sriram was conducting an experiment in which the average of 11 observations came to be 92, while the average of first five observations was 89, and that of the last five was 86. What was the measure of the 6th observation ?
Options- A. 134
- B. 137
- C. 139
- D. 141 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 137
Explanation:
- 9. 20 men went to a restaurant. Ninteen of them paid Rs.70 each and the twentieth man paid Rs.90.25 more than the average of all the 20 men. What is the total bill ?
Options- A. Rs. 1495
- B. Rs. 548
- C. Rs. 850
- D. Rs. 1750 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: Rs. 1495
Explanation:
Let the average bill paid by twenty members = 'x'
But 19 men paid each = Rs. 70
20th man paid Rs. 90.25 more than the avg bill of 20 = x + 90.25
20x = 19(70) + x + 90.25
19x = 1330 + 90.25
19x = 1420.25
x = 1420.25/19 = Rs. 74.75
But the total bill = 20 x 74.75 = Rs. 1495.
- 10. A batsman scores 26 runs and increases his average from 14 to 15. Find the runs to be made if he wants top increasing the average to 19 in the same match ?
Options- A. 74
- B. 79
- C. 72
- D. 60 Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 74
Explanation:
Number of runs scored more to increse the ratio by 1 is 26 - 14 = 12
To raise the average by one (from 14 to 15), he scored 12 more than the existing average.
Therefore, to raise the average by five (from 14 to 19), he should score 12 x 5 = 60 more than the existing average. Thus he should score 14 + 60 = 74.
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