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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

  • 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}

  • 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

  • 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}

  • 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}

  • 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

  • 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)