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Arithmetic : Level 3 Test -6

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Question 1
A stockiest wants to make some profit by selling sugar. He contemplates about various methods. Which of the following would maximize his profit? I.  Sell sugar at 10% profit. II. Use 900 g of weight instead of 1 kg. III. Mix 10% impurities in sugar and selling sugar at cost price. IV. Increase the price by 5% and reduce weights by 5%.
I or III
II, III and IV
Profits are same
Question 1 Explanation: 
Profit percentage in each case is
(i) 10%
(ii) {Error x 100}/wrong weight = (100 x 100)/ 900 =100/9 %
(iii) [{100 – (100/1.1)}/ 100/1.1] x 100 = 10 %
(iv) (105)/95 = 21/19%
Hence, b is the right option
Question 2
A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?
66 2/3%
Question 2 Explanation: 
Profit percentage = 20%.
Selling Price = 1.2 x CP (Cost Price).
This profit is made after the loss due to selling 16 articles at the price of 12.
The loss would be (16 – 12)/16 = 25%.
Therefore, SP x 0.75 = 1.2CP
SP = 1.6CP.
His actual Selling Price, SP = 0.8MP (Marked Price)
So, 0.8MP = 1.6CP or MP = 2CP.
Hence, Marked Price was 100% above his Cost Price.
Question 3
A ship leaves on a long voyage. When it is 18 miles from the shore, a seaplane, whose speed is ten times that of the ship, is sent to deliver mail. How far from the shore does the seaplane catch up with the ship?
24 miles
25 miles
22 miles
20 miles
Question 3 Explanation: 
Distance between the ship and the seaplane is 18 miles
Given that they are travelling in the same direction,
So, their relative speed would be 9 times the speed of the ship
Therefore, the time taken by seaplane = 18/9s = 2/s hours.
Now, the ship covers s miles in an hour. In 2/s hours it would cover 2 miles.
When the seaplane catches up with the ship, it would be 18+2 = 20 miles from the shore.
Question 4
There is a leak in the bottom of the tank. This leak can empty a full tank in 8 hours. When the tank is full, a tap is opened into the tank which admits 6 liters per hour and the tank is now emptied in 12 hours. What is the capacity of the tank?
28.8 liters
36 liters
144 liters
Cannot be determined
Question 4 Explanation: 
The leak can empty the tank in 8 hours,
Work done by leak in one hour = 1/8.
And it’s given that the leak along with the tap can empty it in 12 hours.
So, 1/n – 1/8 = 1/12 (where n is the time taken by the tap to fill the tank).
On solving,
1/n = 1/24 or n = 24.
Therefore, we can say that tap can fill the tank in 24 hours.
Since the tap fill 6 liters per hour,
It will fill exactly fill (6 x 24) = 144 litres in 24 hours
The capacity of the tank is 144 Litres.
Question 5
The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 15 kmph, 16 kmph, 17 kmph, and 18 kmph respectively. What is the ratio of the time taken by B to than taken by D?
5 : 16
5 : 17
9 : 8
8 : 9
Question 5 Explanation: 
As, time is inversely proportional to the speed and it is a relay race,
all the runners ran the same distance.  For a same distance,
(Ratio of Times Taken) = 1/(Ratio of Speeds).
Hence, Ratio of times taken by B and D = 18 : 16 = 9 : 8.
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