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## Number System: Level 2 Test - 10

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Question 1 |

Ten years ago, sum of ages of the members of a joint family of eight people is 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

23 years | |

22 years | |

21 years | |

24 years |

Question 1 Explanation:

The total age of all the eight people in the family = 231

As per the information given in the question, the total age of all the people in the family = 231 + 3 × 8 – 60 + 0 = 195

Similarly the total age of the people in the family four years ago = 195 + 3 × 8 – 60 + 0 = 159.

Therefore the current average age of all the people in the family 159 +32/8 =24

As per the information given in the question, the total age of all the people in the family = 231 + 3 × 8 – 60 + 0 = 195

Similarly the total age of the people in the family four years ago = 195 + 3 × 8 – 60 + 0 = 159.

Therefore the current average age of all the people in the family 159 +32/8 =24

Question 2 |

Shyama and Ramesh walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Ramesh’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Ramesh (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up?

40 | |

50 | |

60 | |

80 |

Question 2 Explanation:

If Shyam takes 1 min for every 3 steps, then he takes 1/3 min for every step.

For 25 steps, he takes 25/3 min,

i.e. 8.33 min. So Ramesh takes1/2 min for every step.

For 20 steps, he takes20/2 min, i.e. 10 min.

Difference between their time = 1.66 min.

Escalator takes 5 steps in 1.66 min and difference in number of steps covered = 5

Speed of escalator is 1 step for 0.33 min, i.e. 3 steps per minute. If escalator is moving,

then Shyam takes 25 steps and escalator also takes 25 steps.

Hence, total number of steps = 50.

For 25 steps, he takes 25/3 min,

i.e. 8.33 min. So Ramesh takes1/2 min for every step.

For 20 steps, he takes20/2 min, i.e. 10 min.

Difference between their time = 1.66 min.

Escalator takes 5 steps in 1.66 min and difference in number of steps covered = 5

Speed of escalator is 1 step for 0.33 min, i.e. 3 steps per minute. If escalator is moving,

then Shyam takes 25 steps and escalator also takes 25 steps.

Hence, total number of steps = 50.

Question 3 |

Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for similar reason. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?

38 | |

31 | |

41 | |

None of these |

Question 3 Explanation:

Let there be x mints originally in the bowl.

Sita took 1/3 but returned 4. So now the bowl has 2/3x + 4 mints.

Fatima took 1/4of the remainder, but returned 3.

So the bowl now has ¾(2/3x +4)+3 mints Eshwari took half of remainder that is 1/2[3/4{2/3x+4}+3]

She returns 2, so the bowl now has ½[3/4{2/3x+4}+3] she returns 2,

so the bowl now has ½[3/4{2/3+4}+3]+2=17

X=48

Short cut: Since Sita was the first person to pick and she picks up1/3 of the mint, but if you see the options, none of the option is a multiple of 3.

Sita took 1/3 but returned 4. So now the bowl has 2/3x + 4 mints.

Fatima took 1/4of the remainder, but returned 3.

So the bowl now has ¾(2/3x +4)+3 mints Eshwari took half of remainder that is 1/2[3/4{2/3x+4}+3]

She returns 2, so the bowl now has ½[3/4{2/3x+4}+3] she returns 2,

so the bowl now has ½[3/4{2/3+4}+3]+2=17

X=48

Short cut: Since Sita was the first person to pick and she picks up1/3 of the mint, but if you see the options, none of the option is a multiple of 3.

Question 4 |

A green light flashes three times per minute and a red light flashes five times in 2 min at regular Intervals. If both lights start together, then how many times do they flash together in each hour?

30 | |

24 | |

20 | |

60 |

Question 4 Explanation:

First light blinks after 20 s. Second light blinks after 24 s.

They blink together after LCM of 20 and 24 = 120 s = 2 min.

Hence, the number of times they blink together in an hour = 30.

They blink together after LCM of 20 and 24 = 120 s = 2 min.

Hence, the number of times they blink together in an hour = 30.

Question 5 |

Out of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. Find the minimum number of boxes containing the same number of oranges is at least

5 | |

103 | |

6 | |

Cannot be determined |

Question 5 Explanation:

Since he has to put minimum 120 oranges and maximum 144 oranges, i.e. 25 oranges need to be filled in 128 boxes with same number of oranges in the boxes.

There are 25 different possibilities if there are 26 boxes, at least 2 boxes contain the same number of oranges (i.e. even if each of the 25 boxes contains a different number of oranges,

the 26th must contain one of these numbers).

Similarly, if there are 51 boxes at least 3 boxes contain the same number of oranges.

Hence at least 6 boxes have same number of oranges for 128 boxes.

There are 25 different possibilities if there are 26 boxes, at least 2 boxes contain the same number of oranges (i.e. even if each of the 25 boxes contains a different number of oranges,

the 26th must contain one of these numbers).

Similarly, if there are 51 boxes at least 3 boxes contain the same number of oranges.

Hence at least 6 boxes have same number of oranges for 128 boxes.

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