If one-third of one-fourth of a number is 15, then three-tenth of that number is:

**A. ** 35

**B. ** 36

**C. ** 45

**D. ** 54

**Answer : ****Option D**

**Explaination / Solution: **

Let the number be *x*.

Then, | 1 | of | 1 | of x = 15 x = 15 x 12 = 180. |

3 | 4 |

So, required number = | 3 | x 180 | = 54. | ||

10 |

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What decimal of an hour is a second ?

**A. ** .0025

**B. ** .0256

**C. ** .00027

**D. ** .000126

**Answer : ****Option C**

**Explaination / Solution: **

Required decimal = | 1 | = | 1 | = .00027 |

60 x 60 | 3600 |

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The cube root of .000216 is:

**A. ** .6

**B. ** .06

**C. ** 77

**D. ** 87

**Answer : ****Option B**

**Explaination / Solution: **

(.000216)^{1/3} | = | 216 | 1/3 | ||

10^{6} |

= | 6 x 6 x 6 | 1/3 | ||

10^{2} x 10^{2} x 10^{2} |

= | 6 |

10^{2} |

= | 6 |

100 |

= 0.06

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Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

**A. ** 2 : 5

**B. ** 3 : 5

**C. ** 4 : 5

**D. ** 6 : 7

**Answer : ****Option C**

**Explaination / Solution: **

Let the third number be *x*.

Then, first number = 120% of x = | 120x | = | 6x |

100 | 5 |

Second number = 150% of x = | 150x | = | 3x |

100 | 2 |

Ratio of first two numbers = | 6x | : | 3x | = 12x : 15x = 4 : 5. | ||

5 | 2 |

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Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

**A. ** 5/11

**B. ** 6/11

**C. ** 7/11

**D. ** 8/11

**Answer : ****Option B**

**Explaination / Solution: **

Part filled by (A + B + C) in 3 minutes = 3 | 1 | + | 1 | + | 1 | = | 3 x | 11 | = | 11 | . | ||||

30 | 20 | 10 | 60 | 20 |

Part filled by C in 3 minutes = | 3 | . |

10 |

Required ratio = | 3 | x | 20 | = | 6 | . | ||

10 | 11 | 11 |

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A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

**A. ** 1/3

**B. ** 1/4

**C. ** 1/5

**D. ** 1/7

**Answer : ****Option C**

**Explaination / Solution: **

Suppose the vessel initially contains 8 litres of liquid.

Let *x* litres of this liquid be replaced with water.

Quantity of water in new mixture = | 3 - | 3x | + x | litres | ||

8 |

Quantity of syrup in new mixture = | 5 - | 5x | litres | ||

8 |

3 - | 3x | + x | = | 5 - | 5x | |||||

8 | 8 |

5*x* + 24 = 40 - 5*x*

10*x* = 16

x = | 8 | . |

5 |

So, part of the mixture replaced = | 8 | x | 1 | = | 1 | . | ||

5 | 8 | 5 |

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In a 100 m race, A can give B 10 m and C 28 m. In the same race B can give C:

**A. ** 18 m

**B. ** 20 m

**C. ** 27 m

**D. ** 9 m

**Answer : ****Option B**

**Explaination / Solution: **

A : B = 100 : 90.

A : C = 100 : 72.

B : C = | B | x | A | = | 90 | x | 100 | = | 90 | . |

A | C | 100 | 72 | 72 |

When B runs 90 m, C runs 72 m.

When B runs 100 m, C runs | 72 | x 100 | m | = 80 m. | |

90 |

B can give C 20 m.

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Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

**A. ** 1/2

**B. ** 2/5

**C. ** 8/15

**D. ** 9/20

**Answer : ****Option D**

**Explaination / Solution: **

Here, S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) = | n(E) | = | 9 | . |

n(S) | 20 |

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The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:

**A. ** Rs. 400

**B. ** Rs. 360

**C. ** Rs. 480

**D. ** Rs. 320

**Answer : ****Option A**

**Explaination / Solution: **

T.D. |
| |||||||||||

| ||||||||||||

| ||||||||||||

= Rs. 400. |

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A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

**A. ** 120 metres

**B. ** 180 metres

**C. ** 324 metres

**D. ** 150 metres

**Answer : ****Option D**

**Explaination / Solution: **

Speed= | 60 x | 5 | m/sec | = | 50 | m/sec. | ||

18 | 3 |

Length of the train = (Speed x Time).

Length of the train = | 50 | x 9 | m = 150 m. | |

3 |

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