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## Number System: Level 2 Test -2

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Question 1 |

The length of hands of a clock is 10 cm and 7 cm respectively. The difference between the distance traversed by their extremities in 3 days 5 h is

4500.67 cm | |

4557.67 cm | |

4691.67 cm | |

4681.67 cm |

Question 1 Explanation:

Distance traversed by the extremity of the minute hand in 1 hour = (2x22)/(7x10)

Distance traversed by the extremity of the minute hand in 3 days and 5 hours i.e 77h=(2x22)/(7x10x77)

Distance traversed by the extremity of the hour - hand in 12 hours = (2 x 22)/(7x7) =44cm

Distance traversed by the extremity of the hour - hand in 77h =44/(12x77)=282.33

Required difference=4840-282.33=4557.67

Distance traversed by the extremity of the minute hand in 3 days and 5 hours i.e 77h=(2x22)/(7x10x77)

Distance traversed by the extremity of the hour - hand in 12 hours = (2 x 22)/(7x7) =44cm

Distance traversed by the extremity of the hour - hand in 77h =44/(12x77)=282.33

Required difference=4840-282.33=4557.67

Question 2 |

Rohit, Harsha and Sanjeev are three typists, who working simultaneously can type 216 pages in four hours. In one hour, Sanjeev can type as many pages more than Harsha as Harsha can type more than Rohit. During a period of five hours, Sanjeev can type as many pages as Rohit can during seven hours. ‘How many pages does each of them type per hour respectively?

14, 17, 20 | |

16, 18, 22 | |

15, 17, 22 | |

15, 18, 21 |

Question 2 Explanation:

Let Rohit's typing in 7 h be

Then, his first hour typing =x/7 pages

Sanjeev's typing in 5 h =

Sanjeev's typing in 1 h =x/5 pages

Harsha's typing in 1 h = (x/5 + x/7) x 1/2 =

4(x/7 + x/5 + 6x/35) = 216

4(18x/35) = 216 = x = 216 x 35 /18 x 4 = 105

Required ratio = 105 /7 :105 x 6/35 :105/5 = 15:18:21

*x*pages.Then, his first hour typing =x/7 pages

Sanjeev's typing in 5 h =

*x*pagesSanjeev's typing in 1 h =x/5 pages

Harsha's typing in 1 h = (x/5 + x/7) x 1/2 =

*6x/35*4(x/7 + x/5 + 6x/35) = 216

4(18x/35) = 216 = x = 216 x 35 /18 x 4 = 105

Required ratio = 105 /7 :105 x 6/35 :105/5 = 15:18:21

Question 3 |

The numbers from 1 to 29 are written side-by-side as follows 1 2 3 4 5 6 7 8 9 10 11 .... 28 29 the resultant number is now divided by 9, Find the remainder of it?

3 | |

1 | |

0 | |

None of these |

Question 3 Explanation:

Sum of digits from numbers 1 to 10 = 46

Sum of digits from numbers 11 to 20 = 56

Sum of digits from numbers 21 to 29 = 63

Sum of digits in given numbers = 46+ 56+ 63=165

Alternate solution: We can use the formula for sum of sum of n natural no. formula I.e [n*(n+1)]/2

Now sum of digits is [29*30]/2=435

Sum of these is: 4+3+5=12

Remainder of this number with 9 is 3.

So, Sum of digits in the number 165 = 12

which gives a remainder of 3 when divided by 9

Sum of digits from numbers 11 to 20 = 56

Sum of digits from numbers 21 to 29 = 63

Sum of digits in given numbers = 46+ 56+ 63=165

Alternate solution: We can use the formula for sum of sum of n natural no. formula I.e [n*(n+1)]/2

Now sum of digits is [29*30]/2=435

Sum of these is: 4+3+5=12

Remainder of this number with 9 is 3.

So, Sum of digits in the number 165 = 12

which gives a remainder of 3 when divided by 9

Question 4 |

Find the value of M and

*N*respectively if M39048458N*is divisible by 11 and 8 , where M and**N*are integers? 7, 8 | |

8, 6 | |

6, 4 | |

5, 4 |

Question 4 Explanation:

A number is divisible by 8 if the number formed by the last three digits is divisible by 8,

ie; 58N is divisible by 8.

Hence, N =4 Again a number is divisible by 11

if the difference between the sum of digits at even place

and sum of digits at the odd places is either 0 or divisible by 11,

= M - N + 9 (M - N) + 9 must be zero or it must be divisible by 11. i.e.

M – N =2

M= 2+4= 6

M= 6, N= 4

ie; 58N is divisible by 8.

Hence, N =4 Again a number is divisible by 11

if the difference between the sum of digits at even place

and sum of digits at the odd places is either 0 or divisible by 11,

*ie,*(M + 9 + 4 + 4 + 8) - (3 + 0 + 8 + 5 + N) = M + 25 - (16 + N)= M - N + 9 (M - N) + 9 must be zero or it must be divisible by 11. i.e.

M – N =2

M= 2+4= 6

M= 6, N= 4

Question 5 |

The difference of the age of the two person is 20 yr. If 5 yr ago, the older one be 5 times as old as the younger one, Find the present age (in yr ) of them

25, 5 | |

30, 10 | |

35, 15 | |

50, 30 |

Question 5 Explanation:

Let’s assume that ages of two persons be x and y them x-y=20--------eq. 1
From second statement x-5=5(y-5)---------------eq. 2
Solving 1 and 2 we get x=30 and y=10

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