# Problems on Average

Q31. The average of marks in English for ten students was found to be 45. Later on, it was discovered that in case of one student, the marks 46 were misread as 64. The correct averaage is

(a) 43.2

(b) 45.5

(c) 49.3

(d) 53.2

**Answer:** (a) 43.2

Total recorded marks = 10 X 45 = 450

Correct Total = (450 - 64 + 46) = 432

∴ Correct average = 432/10 = 43.2

Q32. The average temperature for Sunday, Monday and Tuesday was 35°C. The average temperature for Monday, Tuesday and Wednessday was 36°C. If the temperature on Wednessday be 37°C, find the temperature on Sunday ?

(a) 33°

(b) 34°

(c) 35°

(d) 36°

**Answer:** (b) 34°

S + M + T | = 35 |

3 |

⇒ S + M + T = 3 X 35° = 105° ------- (1)

And | M + T + W | = 36 |

3 |

⇒ M + T + W = 3 X 36° = 108° ------ (2)

Again W = 37°

(2) ⇒ M + T + 37° = 108°

⇒ M + T = 71° ----- (3)

(1)⇒ S + M + T = 105°

⇒ S + 71° = 105°

⇒ S = 34°

Q33. The average of five numbers is 26. If one number is excluded, the average become 28. Find the excluded number.

(a) 14

(b) 15

(c) 17

(d) 18

**Answer:** (d) 18

Sum of five numbers = 5 X 26 = 130

Sum of four numbers = 4 X 28 = 112

∴ Excluded no = 130 - 112 = 18

Q34. If the average of x numbers is y^{2} and that of y number is x^{2}, then the average of (x+y) number is

(a) x + y

(b) xy^{2}

(c) xy

(d) (xy)^{2}

**Answer:** (c) xy

Sum of x numbers = xy^{2}

Sum of y numbers = yx^{2}

Sum of (x+y) numbers = xy^{2} + yx^{2} = xy (x+y)

∴ Average of (x+y) numbers = | xy (x+y) | = xy |

x+y |

Q35. The average of 6 numbers is 30. If the average of first four is 25 and that of last three is 40, the fourth number is ?

(a) 30

(b) 35

(c) 40

(d) 45

**Answer:** (c) 40

Let the nos be x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6}

A/Q x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} = 6 X 30 = 180 ---- (1)

x_{1} + x_{2} + x_{3} + x_{4} = 4 X 25 = 100 ----- (2)

x_{4} + x_{5} + x_{6} = 3 X 40 = 120 ----- (3)

(1) - (2) ⇒ x_{5} + x_{6} = 180 - 100 = 80 ------ (4)

(3) - (4) ⇒ x_{4} = 120 - 80 = 40

Q36. What is the least number to be added to 235 to make it a perfect square ?

(a) 14

(b) 15

(c) 17

(d) 21

**Answer:** (d) 21

1 ) ¯2 3 ¯5 ( 15

1

25) 135 (

125

10

∴ Required no = 16^{2} - 235 = 256 - 235 = 21

Q37. What is the least number to be substructed from 235 to make it a perfect square ?

(a) 7

(b) 10

(c) 15

(d) 17

**Answer:** (b) 10

1 ) ¯2 3 ¯5 ( 15

1

25) 135 (

125

10

Perfect square is = 15^{2}

∴ Required no = 235 - 15^{2} = 235 - 225 = 10

Q38. If a = √5 + √5 + √5 + ...... α , then what is the value of a

(a) 2.29

(b) 3.19

(c) 3.82

(d) 4.10

**Answer:** (a) 2.29

a = √(5 + a)

⇒ a^{2} = 5 + a

⇒ a^{2} - a - 5 = 0

a = | -(-1) ± √[(-1)^{2} - 4 . 1 . (-5)] |

2 |

= | 1 ± √(1 + 20) |

2 |

= | 1 ± √21 |

2 |

= | 1 + 4.58 |

2 |

= | 5.58 |

2 |

= 2.29

Q39. What is the smallest number by which 6750 must be divided to make it a perfect cube ?

(a) 2

(b) 3

(c) 4

(d) 5

**Answer:** (a) 2

2|6750 |

3|3375 |

3|1125 |

3|375 |

5|125 |

5|25 |

5 |

6750 = 2 X 3 X 3 X 3 X 5 X 5 X 5

∴ Required no = 2

Q40. Number of digits in the square root of 625686734489 is

(a) 5

(b) 6

(c) 8

(d) 9

**Answer:** (b) 6

It is a number with 6 pairs of digit.

∴ Number of digits in the square root is 6.