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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.Â 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 | |

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 â€“ (100/1.1)}/ 100/1.1] x 100 = 10 %

(iv) (105)/95 = 21/19%

Hence, b is the right option

(i) 10%

(ii) {Error x 100}/wrong weight = (100 x 100)/ 900 =100/9 %

(iii) [{100 â€“ (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?

100% | |

80% | |

75% | |

66 ^{2}/_{3}% |

Question 2 Explanation:

Profit percentage = 20%.

Selling Price = 1.2 x CP

This profit is made after the loss due to selling 16 articles at the price of 12.

The loss would be (16 â€“ 12)/16 = 25%.

Therefore, SP x 0.75 = 1.2CP

SP = 1.6CP.

His actual Selling Price, SP = 0.8MP

So, 0.8MP = 1.6CP or MP = 2CP.

Hence, Marked Price was 100% above his Cost Price.

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 â€“ 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.

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 itâ€™s given that the leak along with the tap can empty it in 12 hours.

So, 1/n â€“ 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.

Work done by leak in one hour = 1/8.

And itâ€™s given that the leak along with the tap can empty it in 12 hours.

So, 1/n â€“ 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. Â 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.

all the runners ran the same distance. Â 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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