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## Arithmetic : Level 2 Test -2

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Question 1 |

A man ordered 4 pairs of black socks and some pairs of brown socks. The price of a black pair is double that of a brown pair. While preparing the bill, the clerk did a mistake and interchanged the number of black and brown pairs. This increased the bill by 50%. The ratio of the number of black and brown pairs of socks in the original order was

4 : 1 | |

2 : 1 | |

1 : 4 | |

1 : 2 |

Question 1 Explanation:

Let us assume that the number of brown pairs purchased by him = p

Let us assume the price of the brown socks = Rs. s

Then the price of the black socks = Rs. 2s

3/2 (4 x 2s + p x s) = p x 2s + 4 x s

12s + 3/2 p x s = 2 x p x s + 4a

12 + 3/2p = 2s + 4

p/2 = 8

p = 16

Therefore, the required ratio is 4/16 = ¼

Let us assume the price of the brown socks = Rs. s

Then the price of the black socks = Rs. 2s

3/2 (4 x 2s + p x s) = p x 2s + 4 x s

12s + 3/2 p x s = 2 x p x s + 4a

12 + 3/2p = 2s + 4

p/2 = 8

p = 16

Therefore, the required ratio is 4/16 = ¼

Question 2 |

Three friends Richa, Anamika andAnkitadivideRs. 1105 amongst them in such a way that if Rs. 10,Rs. 20 and Rs. 15 are removed from the sums thatRicha, Anamika and Ankitareceive respectively, then the share of the sums that they get will be in the ratio of 11 : 18 : 24. How much did Anamika receive?

Rs. 495 | |

Rs. 510 | |

Rs. 480 | |

Rs. 375 |

Question 2 Explanation:

Total sum of money = 1105

Rs 10,Rs.20 and Rs. 15 are removed from the sum

Final ratio of sum they received = 11: 18 : 24

Therefore the final sum would be

= 11x + 10 + 18x + 20 + 24x + 15

= 1105= 53x + 45

x =20

Therefore, the amount received by Anamika will be = 24x + 15 = 495

Rs 10,Rs.20 and Rs. 15 are removed from the sum

Final ratio of sum they received = 11: 18 : 24

Therefore the final sum would be

= 11x + 10 + 18x + 20 + 24x + 15

= 1105= 53x + 45

x =20

Therefore, the amount received by Anamika will be = 24x + 15 = 495

Question 3 |

Two vessels contain spirit of 0.5 and 0.75 concentrations. If 2 L from the first vessel and 3 L from the second vessel are mixed, then what will be the ratio of the spirit and the water in the resultant solution?

15 : 17 | |

7 : 17 | |

13 : 7 | |

17 : 15 |

Question 3 Explanation:

In vessel 1

Spirit = 0.5

Water = 0.5

In vessel 2

Spirit = 0.75

Water = 0.25

In first vessel the ratio is 1: 1

And in second vessel the ratio is 3 : 1

So the final ratio spirit: water in the resultant solution = (½ x 2 + ¾ x 3 ) / (1/2 x 2 + ¼ x 3 ) = 13/7

Spirit = 0.5

Water = 0.5

In vessel 2

Spirit = 0.75

Water = 0.25

In first vessel the ratio is 1: 1

And in second vessel the ratio is 3 : 1

So the final ratio spirit: water in the resultant solution = (½ x 2 + ¾ x 3 ) / (1/2 x 2 + ¼ x 3 ) = 13/7

Question 4 |

In a mixture of 60 L, the ratio of milk and water is 2 : 1. If the ratio of milk and water is to be 1 : 2, then the amount of water to be further added must be:

40 L | |

30 L | |

20 L | |

60 L |

Question 4 Explanation:

The ratio of milk and water is 2 : 1

Therefore the quantity of water is 1/3 x 60 = 20 L1

Quantity of milk = 2/3 x 60 = 40 L1

Now let us suppose the quantity of water which is to be added = s L1

Then 40 / s + 20 = ½1

s = 60 L1

Therefore the quantity of water is 1/3 x 60 = 20 L1

Quantity of milk = 2/3 x 60 = 40 L1

Now let us suppose the quantity of water which is to be added = s L1

Then 40 / s + 20 = ½1

s = 60 L1

Question 5 |

A man left one-half of the property for his wife. One-third to his son and the remainder to his daughter and her share were worth Rs. 45000, how much money did the man leave

Rs. 245000 | |

Rs. 260000 | |

Rs. 270000 | |

Rs. 275000 |

Question 5 Explanation:

Let us suppose the property left by the man = Rs. P1

Then the share of his daughter would be = P – P/2 –P/31

Also given that the money was = 450001

So 45000 = p/61

Therefore P = Rs. 270000

Then the share of his daughter would be = P – P/2 –P/31

Also given that the money was = 450001

So 45000 = p/61

Therefore P = Rs. 270000

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