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## Arithmetic : Level 2 Test - 1

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Question 1 |

Two taps A and B can fill a cistern in 12 min and 15 min respectively. They are opened together but after a few min, A is turned off and the rest of the cistern is filled by B in 5 min. After how many minutes was A turned off?

4 min | |

7 min | |

6 min | |

None of these |

Question 1 Explanation:

Let the turn off time of A = p min

Now we have case when the pipe was closed: we know that for the last 5 min B worked alone

hence 5/15 = 1/3

If 1/3

then 2/3

A and B can full the tank in 1/12+1/15 = 9/60 = 1/ T

That means in 20/3 A and B can full the complete tank

Hence for the time for which A is on = 2/3 rd of the tank filled = 2/3 * 20/3 = 40/9 = 4

Hence answer is none of these i.e option D.

Now we have case when the pipe was closed: we know that for the last 5 min B worked alone

hence 5/15 = 1/3

^{rd}of the tank is filled by b aloneIf 1/3

^{rd}of the tank is filled by B alone,then 2/3

^{rd}of the tank is filled by A & B togetherA and B can full the tank in 1/12+1/15 = 9/60 = 1/ T

That means in 20/3 A and B can full the complete tank

Hence for the time for which A is on = 2/3 rd of the tank filled = 2/3 * 20/3 = 40/9 = 4

^{4 }/_{9}Hence answer is none of these i.e option D.

Question 2 |

A sum of Rs. 30600 is divided between Richa and Atish, who are respectively 18 and 19 yr old, in such a way that if their shares are invested at 4% per annum compounded annually, they shall receive the same amount on reaching 21 yr of age. What is the share of Richa?

Rs. 16000 | |

Rs. 15000 | |

Rs. 15600 | |

Rs. 14600 |

Question 2 Explanation:

Let the share of Richa is p

Then the share of Atish is (30600 – p)

Therefore p x (1+4/100)

p x 104/100 = 30500 –p

p x 104/100 + p = 30500

(204/100)p = 30600

p = Rs.15000

Then the share of Atish is (30600 – p)

Therefore p x (1+4/100)

^{3}=(30600 – p)(1+4/100)^{2}p x 104/100 = 30500 –p

p x 104/100 + p = 30500

(204/100)p = 30600

p = Rs.15000

Question 3 |

A man divided his share between his sons A and B in such a way that the interest received by A at 15% per annum for 3 yr is double the interest received by B at 12% per annum for 5 yr. It what ratio was hisshare divided?

2/3 | |

8/3 | |

3/8 | |

3/2 |

Question 3 Explanation:

Let the share of a A = Rs p

Let the share of a B = Rs q

Therefore from the question, the equation for simple interest received by the two sons is as follows:

(p x 15 x 3) / 100 = 2 x (q x 15 x 3) / 100

p/q = (2 x 12 x 5 )/ 15 x 3 = 8/3

Let the share of a B = Rs q

Therefore from the question, the equation for simple interest received by the two sons is as follows:

(p x 15 x 3) / 100 = 2 x (q x 15 x 3) / 100

p/q = (2 x 12 x 5 )/ 15 x 3 = 8/3

Question 4 |

Ms Sharma's expenditure and savings are in the ratio of 3: 2. Her income increases by 10%. Her expenditure also increases by 12%. By what percentage do her savings increase?

7% | |

6% | |

13% | |

11% |

Question 4 Explanation:

Let Ms. Sharma’s saving = 2s

Let Ms. Sharma’s expenditure = 3s

Therefore, his initial total income becomes 5s

Now her income increases by 10 % so

New income will be 5.5s

Her expenditure increases by 12 % and therefore

Her new expenditure 3s x 12% = 3.36s

Therefore, her new saving is 5.5s – 3.36s = 2.14s

Percentage Increase in savings = (2.14s – 2s)/2s x 100 = 7%

Let Ms. Sharma’s expenditure = 3s

Therefore, his initial total income becomes 5s

Now her income increases by 10 % so

New income will be 5.5s

Her expenditure increases by 12 % and therefore

Her new expenditure 3s x 12% = 3.36s

Therefore, her new saving is 5.5s – 3.36s = 2.14s

Percentage Increase in savings = (2.14s – 2s)/2s x 100 = 7%

Question 5 |

The ratio of milk to water in three containers of equal capacity is 3 : 2, 7 : 3 and 11 : 4 respectively. The three containers are mixed together. What is the ratio of milk to water after mixing?

38 : 8 | |

21: 9 | |

61: 29 | |

41: 18 |

Question 5 Explanation:

To do these types first let the value of the total mixture
Let it be 30 l

We take 30 l for simple calculations and 30 is the common factor of 5, 10, 15

Now therefore the Quantity of Milk after mixing will be (3/5 + 7/10 + 11/15) x 30 = 61 l

Now the Quantity of water after mixing will be

(2/5 + 3/10 + 4/15) x 30 = 29 l

Therefore the required ratio will be = 61 : 29

We take 30 l for simple calculations and 30 is the common factor of 5, 10, 15

Now therefore the Quantity of Milk after mixing will be (3/5 + 7/10 + 11/15) x 30 = 61 l

Now the Quantity of water after mixing will be

(2/5 + 3/10 + 4/15) x 30 = 29 l

Therefore the required ratio will be = 61 : 29

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