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Arithmetic : Level 1 Test -9

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Question 1
Out of the total production of iron from haematite, an ore of iron, 20% of the ore gets wasted. Out of the remaining iron, only 25% is pure iron. If the pure iron obtained in a year from a mine of haematite was 80000 kg, then the quantity of haematite mined in the year is
400000 kg
500000 kg
450000 kg
600000 kg
Question 1 Explanation: 
Let the quantity of the hematite per year = 100 kg
Total wastage = 20% = 20 kg
Therefore the left ore is 80 kg
25% of 80 is the pure iron i.e.= 20 kg is the pure iron
But we are given by that the total extraction of pure iron in an year is= 80000kg
So therefore if 20 kg was the pure iron the quantity of whole mixture was=100 kg
So when 80000kg of iron is extracted the quantity would be = 100/20 x 80000 = 400000kg
Question 2
Men, women and children are employed to do a work in the proportion of 1 : 2 : 3 and their wages are in the proportion of 6 : 3 : 2. When 50 men are employed, total wages of all amount to Rs. 4500. What is the weekly wages paid to a man, a woman and a child, in rupees?
210, 105, 80
210, 105, 70
210, 105, 90
200, 105, 70
Question 2 Explanation: 
The number of men employed =50
The ratio of men : women : children = 1:2:3
Therefore the number of women =100
The number of children = 150
Now the wages are in the ratio of 6 : 3 : 2
Let their wages be 6w , 3w, 2w
Now the total wages amounts to 4500
So therefore (6w x 50) + (3w x 100) + (2w x 150) = 4500
900w = 4500
therefore the daily wage for men = Rs. 30
therefore the daily wage for women = Rs. 15
therefore the daily wage for children = Rs. 10
Weekly wage of a man, a woman and a child= Rs. 210 , Rs. 105 , Rs. 70
Question 3
One year ago, the ratio between Mahesh's and Suresh's salaries was 3: 5. The ratio of their individual salaries of last year and present year are 2: 3 and 4: 5 respectively. If their total salaries for the present year are Rs. 43000, what is the present salary of Mahesh?
Question 3 Explanation: 
Let the present and last year salary of Mahesh's and Suresh's be p, p' and q, q' respectively.
According to the given condition,
p' / q' = 3/5
p’ / p = 2/3
q' / q = 4/5
{p' / p} / {q' / q} = {2/3} / {4/5}
p' / q'  x  q / p = 10/12
3/5 x q/p = 10/12
q/p = 50/36
p + q =43000
p + 50/36p =43000
p = {43000 x 36} / 86 = Rs. 18000
Question 4
A certain tank can be filled by pipes A and B separately in 4 and 5 min respectively, whereas pipe C can empty in 3 min. How long will it take to fill or empty the 4/5th full tank, if all the three pipes are opened together?
25/7 min to fill
6 2/7min to fill
66/7 min to fill
15/7 min to fill
Question 4 Explanation: 
Pipe A filled the tank in 4 min
Pipe B filled the tank in 5 min
Pipe C empty the tank in 3 min
Tank can filled in 1 minute when all pipes runs together would be = ¼ + 1/5 - 1/3 = 7/60
If 7/60 part is filled in 1 minute
Then 4/5th part of the tank would be filled in 60/7 x 4/5 = 48/7 = 66/7 min
Question 5
When the waste pipe is closed, two taps can separately fill a cistern in 10 and 12 min respectively. When the waste pipe is opened, they together fill it in 15 min. How long does it take the waste pipe to empty the cistern, when the taps are closed?
7 min 10 s
8 min 34 s
12 min
10 min
Question 5 Explanation: 
In one minute, when the waste pipe is closed, work done by taps {1/10 + 1/12}
In one minute, when the waste pipe is open, work done by the pipes = 1/15
So work done by the waste pipe in one minute = 1/15 – (1/10 + 1/12)  = -14/120
From this we can that the pipe will empty the cistern in 8 minute and 34 sec.
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