# Simplification

## Simplification

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Question 1 |

A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

45 | |

60 | |

75 | |

90 |

Question 1 Explanation:

Let number of notes of each denomination be x.
Then x + 5x + 10x = 480 ==> 16x = 480 ==> x = 30.
Hence, total number of notes = 3x = 90.

Question 2 |

There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:

20 | |

80 | |

100 | |

200 |

Question 2 Explanation:

Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.

Question 3 |

One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?

Rs. 30,000 | |

Rs. 50,000 | |

Rs. 60,000 | |

Rs. 90,000 |

Question 3 Explanation:

Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,
1/3x = 1/2(150000 - x) =>x/3+x/2= 75000 =>5x/6= 75000 => x =(75000 x 6)/5= 90000
Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000

Question 4 |

In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?

160 | |

175 | |

180 | |

195 |

Question 4 Explanation:

Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.

Question 5 |

A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:

22 | |

24 | |

26 | |

28 |

Question 5 Explanation:

Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140 x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26

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