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Arithmetic : Level 3 Test -10

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Question 1
Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?
A
550
B
580
C
540
D
570
Question 1 Explanation:
Let the fixed cost = R
Let variable cost be = S
17500 = R + 25S … (i)
30000 = R + 50S … (ii)
Solving the equation (i) and (ii), we get
R = 5000, S = 500
Let the average expense of the 100 boarders =Z
Then 100 × Z = 5000 + 500 × 100
∴Z = 550.
Question 2
Two typists undertake to do a job. The second typist begins working one hour after the first. Three hours after the first typist has begun working, there is still 9/20 of the work to be done. When the assignment is completed, it turns out that each typist has done half the work. How many hours would it take each one to do the whole job individually ?
A
12 hr and 8 hr
B
8 hr and 5.6 hr
C
10 hr and 8 hr
D
5 hr and 4 hr
Question 2 Explanation:
Time taken by first typist = t1
Time taken by second typist = t2
First typist worked for 3 hours
And the second typist worked for 2 hours
Therefore their total work done = 3/t1 + 2/t2 = 11/20 …………………………………..1
Also when the assignment is completed, it turns out that each typist has done half the work.
Therefore t1/2 – t2/2 = 1……………………………….2
By 1 and 2
t1 = 10 hours
t 2 = 8 hours
Question 3
A shipping clerk has five boxes of different but unknown weights each weighing less than 100 kg. The clerk weights the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight of the heaviest box?
A
60 kg
B
62 kg
C
64 kg
D
Cannot be determined
Question 3 Explanation:
The answer will be between 60 t0 64 both excluded
Because if the weight of the heaviest box is 60 then other box should be of 61
60 + 61 = 121
Which is not true?
If the heaviest box is of 64 kg then other would be of 57 which is also not true
So the right answer is 62
62 is the correct answer because the other boxes shall be 59, 54, 58, 56.
These will give all the totals given above.
Question 4
The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.
A
55
B
60
C
62
D
Cannot be determined
Question 4 Explanation:
Total marks scored = (80 × 10) = 800.
Total Marks by excluding the papers in which he scored
highest and the lowest = (81 × 8) = 648.
Therefore his total of lowest and highest = (800 – 648) = 152.
Given that the highest score is 92, his lowest score is (152 – 92) = 60.
Question 5
A yearly payment to the servant is Rs. 90 plus one turban. The servant leaves the job after 9 months and receives Rs. 65 and a turban. Then find the price of the turban.
A
Rs. 10
B
Rs. 15
C
Rs. 7.50
D
Cannot be determined
Question 5 Explanation:
Let the cost of the turban be T.
Yearly payment = Rs. 90
Hence, total payment for one year =  Rs. 90 + T.
So the payment for 9 months should be
3/4(90 + T).( 9 months  is ¾ of 12)
But this is equal to
(65 + T).
Equating the two, we get T = Rs. 10.
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