## Arithmetic Aptitude 5

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Question 1 |

The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 45. What is the difference between the two digits of that number?

5 | |

7 | |

6 | |

None of these |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 1 Explanation:

Let the ten’s digit be x and unit’s digit be y Then (10x + y) – (10y + x) = 45 9(x – y) = 45 x – y = 5

Question 2 |

A two-digit number is such that the product of the digits is 12. When 9 is subtracted from the number, the digits are reversed. The number is:

34 | |

62 | |

43 | |

26 |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 2 Explanation:

Let the ten’s and unit’s digit be x and y. Then 10x + - 9 = 10 x + x 10x2 + 12 -9x = 120 + x2 9x2 – 9x – 108 = 0 x2 –x – 12 = 0 x2 –4x + 3x – 12 = 0 (x – 4) (x + 3) = 0 Therefore x = 4 Hence the required no. is 43

Question 3 |

Find a positive number which when increased by 16 is equal to 80 times the reciprocal of the number

20 | |

-4 | |

-10 | |

4 |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 3 Explanation:

Let the number be x. Then x + 16 = 80 * (1/x) x^{2}+ 16x – 80 = 0 x^{2}+ 20x – 4x – 80 =0 (x + 20) (x -4) Therefore x = 4

Question 4 |

What is the sum of two consecutive odd numbers, the difference of whose squares is 56?

30 | |

28 | |

34 | |

32 |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 4 Explanation:

Let the no. be x and (x +2). Then (x +2)2 – x2 = 56 4x + 4 = 56 x + 1 = 14 x = 13 Sum of numbers = x + (x +2) = 28

Question 5 |

The product of two numbers is 108 and the sum of their squares is 225. The difference of the number is:

5 | |

4 | |

3 | |

None of these |

**Arithmetic Aptitude 5**

**Numbers**

**Discuss it**

Question 5 Explanation:

Let the numbers be x and y. Then xy = 108 and x^{2}+ y^{2}= 225 (x –y)^{2}= x^{2}+ y^{2}– 2xy (x –y)^{2}= 225 – 216 (x –y)^{2}= 9 Therefore (x –y) = 3

There are 5 questions to complete.