Average problems
- 1. 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 Discuss
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
- 2. 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 Discuss
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.
- 3. 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 Discuss
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.
- 4. 16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children of group B?
Options- A. 233/3
- B. 243/4
- C. 254/5
- D. 345/7 Discuss
Correct Answer: 233/3
Explanation:
Required average = [(76 * 16) - (75 * 10)] / 6 = (1216 - 750)/6 = 466/3 = 233 /3.
- 5. The average age of the boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is :
Options- A. 15
- B. 20
- C. 21
- D. data inadequate Discuss
Correct Answer: data inadequate
Explanation:
Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given.
So, the data provided is inadequate.
- 6. What is the average of four tenths and five thousandths
Options- A. 25002
- B. 2502
- C. 0.2025
- D. none Discuss
Correct Answer: 0.2025
Explanation:
Four tenths = 0.4
Five thousandths = 0.005
The average is (0.4 + 0.005)/2 = 0.2025
- 7. The average of any 5 consecutive odd natural numbers is k . If two more such numbers , just next to the previous 5 numbers are added , the new average becomes
Options- A. 2(k+1)
- B. 2k-3
- C. 2k+1
- D. k+2 Discuss
Correct Answer: k+2
Explanation:
The 5 consecutive odd numbers whose average is k are (k-4), (k-2), k, (k+2), (k+4)
Again the average of (k-4), (k-2), k, (k+2), (k+4), (k+6), (k+8) is (k+2)
- 8. The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then :
Options- A. x = y + z
- B. 2x = y + z
- C. 3x = 2y - 2z
- D. none of these Discuss
Correct Answer: 2x = y + z
Explanation:
Clearly, we have : x = (3y + 3z ) / 6 or 2x = y + z.
- 9. In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is :
Options- A. 21
- B. 20
- C. 22
- D. None of these Discuss
Correct Answer: 20
Explanation:
It is the same as a person with 20 years more age replaces an existing person of the group ( or village)
Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village.
Alternatively : ( n x 42 ) + 20 = ( n x 43 )
=> n=20
- 10. The average expenditure of the hotel when there are 10 guests is Rs. 60 per guests and the average expenditure is Rs.40 when there are 20 Guests. If it is known that there are some fixed expenses irrespective of the number of guests then the average expenditure per guest whe there are 40 guests in the hotel.
Options- A. Rs. 30
- B. Rs. 25
- C. Rs. 20
- D. can't be determined Discuss
Correct Answer: Rs. 30
Explanation:
Let the fixed expenditure of the hotel be Rs.x and the variable expenditure ( which is dependent on the guest ) is Rs.y , then
x + 10y = 600 ---------(1)
x + 20y = 800 ----------(2)
From (1) & (2)
10y = 200
=> y = Rs. 20 and x= 400
Hence the total expenditure when there are 40 guests = 400 + 40 x 20 = 1200
Therefore, average expenditure = 1200/40 = Rs. 30
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