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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

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

w=5

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

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

w=5

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?

19000 | |

18000 | |

16000 | |

15500 |

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

pâ€™ / p = 2/3

q' / q = 4/5

{p' / p} / {q' / q} = {2/3} / {4/5}

p' / q'Â xÂ 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

According to the given condition,

p' / q' = 3/5

pâ€™ / p = 2/3

q' / q = 4/5

{p' / p} / {q' / q} = {2/3} / {4/5}

p' / q'Â xÂ 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?

2 ^{5}/_{7} min to fill | |

6 ^{2}/_{7}min to fill | |

6 ^{6}/_{7} min to fill | |

1 ^{5}/_{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 = Â¼ + 1/5 - 1/3 = 7/60

If 7/60 part is filled in 1 minute

Then 4/5

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 = Â¼ + 1/5 - 1/3 = 7/60

If 7/60 part is filled in 1 minute

Then 4/5

^{th}part of the tank would be filled in 60/7 x 4/5 = 48/7 = 6^{6}/_{7}minQuestion 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 â€“ (1/10 + 1/12)Â = -14/120

From this we can that the pipe will empty the cistern in 8 minute and 34 sec.

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 â€“ (1/10 + 1/12)Â = -14/120

From this we can that the pipe will empty the cistern in 8 minute and 34 sec.

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