A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

**A. ** 45 km/hr

**B. ** 50 km/hr

**C. ** 54 km/hr

**D. ** 55 km/hr

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

**Explaination / Solution: **

Speed of the train relative to man = | 125 | m/sec | |

10 |

= | 25 | m/sec. | |

2 |

= | 25 | x | 18 | km/hr | |

2 | 5 |

= 45 km/hr.

Let the speed of the train be *x* km/hr. Then, relative speed = (*x* - 5) km/hr.

*x* - 5 = 45 *x* = 50 km/hr.

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Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is:

**A. ** 173 m

**B. ** 200 m

**C. ** 273 m

**D. ** 300 m

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

**Explaination / Solution: **

Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, ACB = 30° and ADB = 45°.

AB | = tan 30° = | 1 | AC = AB x √3 = 100√3 m. |

AC | √3 |

AB | = tan 45° = 1 AD = AB = 100 m. |

AD |

CD = (AC + AD) | = (100√3 + 100) m |

= 100(√3 + 1) | |

= (100 x 2.73) m | |

= 273 m. |

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The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

**A. ** 2.3 m

**B. ** 4.6 m

**C. ** 7.8 m

**D. ** 9.2 m

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

**Explaination / Solution: **

Let AB be the wall and BC be the ladder.

Then, ACB = 60º and AC = 4.6 m.

AC | = cos 60º = | 1 |

BC | 2 |

BC | = 2 x AC |

= (2 x 4.6) m | |

= 9.2 m. |

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A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

**A. ** Rs. 650

**B. ** Rs. 690

**C. ** Rs. 698

**D. ** Rs. 700

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

**Explaination / Solution: **

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

Principal = Rs. (815 - 117) = Rs. 698.

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Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B?

**A. ** Rs. 6400

**B. ** Rs. 6500

**C. ** Rs. 7200

**D. ** Rs. 7500

**E. ** None of these

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

**Explaination / Solution: **

Let the sum invested in Scheme A be Rs. *x* and that in Scheme B be Rs. (13900 - *x*).

Then, | x x 14 x 2 | + | (13900 - x) x 11 x 2 | = 3508 | ||||

100 | 100 |

28*x* - 22*x* = 350800 - (13900 x 22)

6*x* = 45000

*x* = 7500.

So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.

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The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

**A. ** 15

**B. ** 16

**C. ** 18

**D. ** 25

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

**Explaination / Solution: **

Let C.P. of each article be Re. 1 C.P. of *x* articles = Rs. *x*.

S.P. of *x* articles = Rs. 20.

Profit = Rs. (20 - *x*).

20 - x | x 100 = 25 | |||

x |

2000 - 100*x* = 25*x*

125*x* = 2000

*x* = 16.

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In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

**A. ** 30%

**B. ** 70%

**C. ** 100%

**D. ** 250%

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

**Explaination / Solution: **

Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.

New C.P. = 125% of Rs. 100 = Rs. 125

New S.P. = Rs. 420.

Profit = Rs. (420 - 125) = Rs. 295.

Required percentage = | 295 | x 100 | % | = | 1475 | % = 70% (approximately). | |

420 | 21 |

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Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. The marks obtained by them are:

**A. ** 39, 30

**B. ** 41, 32

**C. ** 42, 33

**D. ** 43, 34

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

**Explaination / Solution: **

Let their marks be (*x* + 9) and *x*.

Then, x + 9 = | 56 | (x + 9 + x) |

100 |

25(*x* + 9) = 14(2*x* + 9)

3*x* = 99

*x* = 33

So, their marks are 42 and 33.

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A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

**A. ** 588 apples

**B. ** 600 apples

**C. ** 672 apples

**D. ** 700 apples

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

**Explaination / Solution: **

Suppose originally he had *x* apples.

Then, (100 - 40)% of *x* = 420.

60 | x x = 420 | |

100 |

x = | 420 x 100 | = 700. | |

60 |

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It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

**A. ** Sunday

**B. ** Saturday

**C. ** Friday

**D. ** Wednesday

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

**Explaination / Solution: **

On 31^{st} December, 2005 it was Saturday.

Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

On 31^{st} December 2009, it was Thursday.

Thus, on 1^{st} Jan, 2010 it is Friday.

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