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Arithmetic : Level 1 Test -3

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Question 1
If Richa offers a discount of 40% on the marked price of her laptop and sold it at its cost price, what was the % mark up?
Question 1 Explanation: 
Richa offers a discount of 40% on the marked price;
therefore, the laptop is sold at 60% of the marked price.
Now after the discount, she sold her laptop on cost price.
Therefore, selling price by giving 40% discount = 60% of marked price (M)
This is equal to the cost price, according to the information given. From this we can say that,
6/10 of mark price = cost price
Mark price = 1.66 of cost price
That is 66.66% more than the cost price
Therefore, the right answer is option C.
Question 2
Richa sold a bag of 20 books and got P-1 as the return and made some profit. She again sold a bag of 40 books and got P-2 as the return (she again made some profit). She realised that the profit by selling 40 books is equal to the selling price of her first bag of books. Then what was the percentage profit she made in the whole transaction?
Question 2 Explanation: 
Let selling price of the single book = Rs. 100
Therefore Selling price of 20 books =  Rs. 2000
Selling price of 40 books =Rs. 4000
She realised that the profit earned by selling 40 books is equal to the selling price of her first bag of books,
so profit of 40 books = Rs. 2000
As we know the selling price is the combination of profit and cost price so
S.P. – C.P. = 2000
4000 – C.P. = 2000
C.P.= 2000
Therefore, the profit percentage 2000/2000 x 100 = 100%
Question 3
A solution of sugar syrup has 15% sugar. Another solution has 5% sugar. How many litres of the second solution must be added to 20 L of the first solution so as to make a solution containing 10% sugar?
10 L
5 L
15 L
20 L
Question 3 Explanation: 
Let the solution which is added from second solution = p L
(15 x 20 + 5 x p) /100 = {10*(20 + p)}/100
300 + 5p = 200 + 10p
p = 100/5=20L
Question 4
An 8 L cylinder contains a mixture of oxygen and nitrogen, the volume of oxygen being 16% of total volume. A few litres of the mixture are released and an equal amount of nitrogen is added. Then, the same amount of the mixture as before is released and replaced by nitrogen for the second time. As result, the oxygen content becomes 9% of total volume.  How many litres of mixture are released each time?
7 L
4 L
2 L
None of these
Question 4 Explanation: 
We will use options for this question.
Let us assume Option (c) i.e. 2L as the amount of the mixture released.
Initial break-up: Oxygen = 1.28 and Nitrogen = 6.72
In 2l of mixture, Oxygen = 0.32 Nitrogen = 1.68
After first release of 2l of mixture,
Amount of oxygen: = 1.28 - 0.32 = 0.96 L
Amount of Nitrogen: 7.04 L
Oxygen released in the second release = 2/8 * 0.96 = 0.24L
Now oxygen left after the second release
= 0.96 - 0.24 = 0.72L which is 9% of 8 L.
So this proves that the mixture release is 2litres
Question 5
Two gallons of a mixture of spirit and water contain 12% of water. They are added to 3 gallons of another mixture, containing 7% of water and half a gallon of water is then added to the whole. Find the percentage of water in the resulting mixture.
Question 5 Explanation: 
2 gallon of mixture of spirit contains 0.24 gallon of water
Another mixture of 3 gallon spirit contains 0.21 gallon of water
1/2 gallon of water is then added to the whole mixture
Therefore, total mixture= 2 + 3 +1/2 = 5.5 gallon which contains 0.95 gallon water.
Therefore 0.95/5.5 x 100 = 190/11 = 173/11

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