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Arithmetic : Level 3 Test -9

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Question 1
I sold two watches for Rs. 300 each, one at the loss of 10% and the other at the profit of 10%. What is the percentage of loss(–) or profit(+) that resulted from the transaction?
(–) 10
Question 1 Explanation: 
We know that when there is effective profit and loss on cost
price then there will be loss on such transactions which
is given by (Profit or loss)2 / 100 = 1%
Question 2
One man can do as much work in one day as a woman can do in 2 days. A child does one third the work in a day as a woman. If an estate-owner hires  39 pairs of hands, men, women and children in the ratio 6 : 5 : 2 and pays them in all Rs. 1113 at the end of the days work. What must the daily wages of a child be, if the wages are proportional to the amount of work done?
Question 2 Explanation: 
39 pairs of hands mean there are 39 people and they are in the ratio of 6 : 5 : 2,
So there will be 18 men, 15 women and 6 children.
One man can do as much work in one day as a woman can
do in 2 days Therefore ratio of the work done by a man: woman = 2: 1.
Similarly The ratio of the work done by a woman: child = 3 : 1.
Hence the ratio of work done in a day by a man: a woman: a child = 6 : 3 : 1.
Therefore the work done by all is in the ratio of (18x6) : (15x3) : (6x1) = 108:45:6.
Total sum of money given to them = Rs. 1113
Therefore they all should be given by Rs.756 for men, 315 for women and Rs.42 for children.
Hence 6 children earn Rs.42 in a day.
So the daily wage of a child should be equal to 42/6 = Rs.7
Question 3
Two towns A and B are 100 km apart. A school is to be built for 100 students of town B and 30 students of Town A. Expenditure on transport is Rs. 1.20 per km per student. If the total expenditure on transport by all 130 students is to be as small as possible, then the school should be built at
33 km from Town A.
33 km from Town B
Town A
Town B
Question 3 Explanation: 
Let the school be built in A
So the expenditure would be = 100 x 1.20 x 100 = Rs. 12000
The expenditure for 30 students of A will be zero
And if the school is build in B
Then the cost would be = Rs. 3600
So if the school would be in Town B,then there will be less expenditure.
Question 4
A man can walk up a moving ‘up’ escalator in 30 s. The same man can walk down this moving ‘up’ escalator in 90 s. Assume that his walking speed is same upwards and downwards. How much time will he take to walk up the escalator, when it is not moving?
30 s
45 s
60 s
90 s
Question 4 Explanation: 
Let the speed of the escalator be r ft per second
Let the speed of the man be s ft per second
Let the length of the escalator be 90 ft.
90/30 = r + s
90/90 = r - s
Adding, 2r = 4, i.e. r = 2.
Therefore Time that the man will take to walk up the escalator
When it is not moving =90/2  or 45 s.
Question 5
A man invests Rs. 3,000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
Rs. 1,200
Rs. 1,300
Rs. 1,500
Rs. 2,000
Question 5 Explanation: 
This can be done by allegation as follows.
Thus, we find that the ratio of the amounts invested in both the rates = 2 : 1.
Since he has invested Rs. 3,000 at 5%, he should further invest
Rs. 1,500 at 8% to earn a total interest of 6% per annum.
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