Problems on Numbers Questions Answers

• 1. Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice of the number

  1. 5
  2. 15
  3. 7.5
  4. 4

  Answer And Explanation

  Answer: Option A

  Explanation:

  Let the number be x.
  7x -15 = 2x + 10 => 5x = 25 => x = 5

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• 2. Sum of a rational number and its reciprocal is 13/6. Find the number

  1. 2
  2. 3/2
  3. 4/2
  4. 5/2

  Answer And Explanation

  Answer: Option B

  Explanation:

  \begin{aligned} => x + \frac{1}{x} = \frac{13}{6} \end{aligned}
  \begin{aligned} => \frac{x^2+1}{x} = \frac{13}{6} \end{aligned}
  \begin{aligned} => 6x^2-13x+6 = 0 \end{aligned}
  
  \begin{aligned} => 6x^2-9x-4x+6 = 0 \end{aligned}
  \begin{aligned} => (3x-2)(2x-3) \end{aligned}
  \begin{aligned} => x = 2/3 or 3/2 \end{aligned}

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• 3. find the number, difference between number and its 3/5 is 50.

  1. 120
  2. 123
  3. 124
  4. 125

  Answer And Explanation

  Answer: Option D

  Explanation:

  Let the number = x,
  Then, x-(3/5)x = 50,
  => (2/5)x = 50 => 2x = 50*5,
  => x = 125

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• 4. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is

  1. 15
  2. 20
  3. 25
  4. 35

  Answer And Explanation

  Answer: Option B

  Explanation:

  Let the numbers be a, b and c.
  Then,
  \begin{aligned}
  a^2 + b^2 + c^2 = 138
  \end{aligned}
  and (ab + bc + ca) = 131
  \begin{aligned}
  (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)
  \end{aligned}
  = 138 + 2 x 131 = 400
  
  \begin{aligned}
  => (a + b + c) = \sqrt{400} = 20.
  \end{aligned}

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• 5. If one third of one fourth of number is 15, then three tenth of number is

  1. 34
  2. 44
  3. 54
  4. 64

  Answer And Explanation

  Answer: Option C

  Explanation:

  Let the number is x,
  \begin{aligned}
  \frac{1}{3} of\frac{1}{4} * x = 15
  \end{aligned}
  
  \begin{aligned}
  => x = 15\times 12 = 180
  \end{aligned}
  
  \begin{aligned}
  => so \frac{3}{10} \times x = \frac{3}{10} \times 180 = 54
  \end{aligned}

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• 6. A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that number

  1. 8
  2. 10
  3. 12
  4. 14

  Answer And Explanation

  Answer: Option A

  Explanation:

  => 3(2x+9) = 75
  => 2x+9 = 25
  => x = 8

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• 7. Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number

  1. 17
  2. 15
  3. 8
  4. 3

  Answer And Explanation

  Answer: Option D

  Explanation:

  If the number is x,
  
  Then, x + 17 = 60/x
  
  x2 + 17x - 60 = 0
  
  (x + 20)(x - 3) = 0
  
  x = 3, -20, so x = 3 (as 3 is positive)

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