Problems on Numbers Questions and Solutions

  • 1. 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 :

    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}

  • 2. A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is

    1. 11
    2. 22
    3. 44
    4. 33
    Answer :

    Option C

    Explanation:

    Let sons age = x. Then, fathers age = 2x.
    12(x—2O) = (2x - 20) so x = 22
    Fathers present age = 44 years

  • 3. 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 :

    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)

  • 4. 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 :

    Option A

    Explanation:

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

  • 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 :

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

    1. 120
    2. 123
    3. 124
    4. 125
    5. 359
    6. 379
    7. 389
    8. 399
    Answer :

    Option

    Explanation:

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

  • 7. Find the number which when multiplied by 15 is increased by 196

    1. 10
    2. 12
    3. 14
    4. 16
    Answer :

    Option C

    Explanation:

    Let the number be x.
    Then, 15x = x + 196
    =› 14 x= 196
    =› x = 14.

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