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Numbers And Number System Test-2

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Numbers And Number System Test-2
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  • Question 1
    1 / -0.25

    The sum of the digits of a two-digit number is 6. If the digits are reversed, the number is decreased by 36. Find the number?

    Solution

    a + b = 6
    (10a + b) –(10b +a) = 36, a –b = 4
    We get a = 5 and b = 1
    So number is 51

  • Question 2
    1 / -0.25

    If the places of last two-digits of a three digit number are interchanged, a new number greater than the original number by 36 is obtained. What is the difference between the last two digits of that number?

    Solution

    let the number be 100a + 10b + c
    (100a + 10b +c) –(100a + 10c +b) = 36
    b –c = 4

  • Question 3
    1 / -0.25

    A number when divided by 143 leaves 31 as the remainder. What will be the remainder when the same number is divided by 13?

    Solution

    A number when divided by 143 leaves 31 as remainder

    The given number is of the form 143x+31=13(11x)+13.2+5 13(11x+2)+5

    Thus, the remainder when the given number is divided by 13 is 5.

  • Question 4
    1 / -0.25

    The numerator of a rational number is 4 less than the denominator. If the numerator is increased by 15 and denominator is decreased by 4, we get 6. Find the rational number?

    Solution

    let the fraction is (p-4)/p
    now, (p -4 + 15)/(p-4) = 6
    we get p = 7
    so fraction = 3/7

  • Question 5
    1 / -0.25

    When a number is added to 20 percent of the second number, we get 150 percent of the second number. Find the ratio between the first and second number?

    Solution

    Let the first number be a and the second number be b . According to the problem:

    a + (20/100)b = (150/100)b .

    Simplifying this equation:

    • a + 0.2b = 1.5b .
    • Subtract 0.2b from both sides:
    • a = 1.5b - 0.2b .
    • a = 1.3b .

    Thus, the ratio of a to b is:

    a /b = 1.3 = 13/10.

    Therefore, the ratio between the first and second number is 13:10 .

  • Question 6
    1 / -0.25

    If two numbers are each divided by the same divisor, the remainders are respectively 3 and 4. If the sum of the two numbers be divided by the same divisor, the remainder is 2. The divisor is

    Solution

    Step-by-Step Solution:

    Step 1: Represent the numbers
    Let the divisor be  d , and the two numbers be  a  and  b .

    • When  a  is divided by  d , remainder = 3.
    • When  b  is divided by  d , remainder = 4.

    Step 2: Sum of the numbers
    The sum of  a  and  b  gives:
    a + b = (some multiple of d) + 7
    When the sum is divided by  d , the remainder is given as 2.
    7 ≡2 (mod d)

    Step 3: Solve for the divisor
    Simplify the equation:
    7 - 2 = 5
    This means  d  must divide 5 evenly.
    The only possible value of  d  is  5 .

    The divisor is  5 .

  • Question 7
    1 / -0.25

    A number gets reduced to its two-third when 24 is subtracted from it. Find oneeighth of the number?

    Solution

    a –24 = 2a/3
    we get a = 72
    so one-eighth of the number = 72/8 = 9

  • Question 8
    1 / -0.25

    Three numbers are in the ratio 4:3:5. If the difference between thrice the third number and the sum of first and second number is 64. Find the difference between the first and third number?

    Solution

    15x –(7x) = 64, we get x = 8
    difference between first and third number = 5x –4x = x = 8

  • Question 9
    1 / -0.25

    One-fifth of a number when subtracted from one –third of the number gives 24. Find the square of the number.

    Solution

    Let the number be a . According to the problem:

    (a/3) - (a/5) = 24.

    To solve this, we need to find a common denominator:

    • Common denominator: 15
    • Rewrite the equation: (5a/15) - (3a/15) = 24

    This simplifies to:

    (2a/15) = 24.

    Now, solving for a gives:

    • 2a = 24 * 15
    • 2a = 360
    • So, a = 180.

    The square of the number is:

    a2 = 1802 = 32400.

  • Question 10
    1 / -0.25

    25% of a number is 2 times 65% of another number. Find the ratio of the second no to the first number?

    Solution

    Let the first number be a and the second number be b . According to the problem:

    0.25a = 2 × (0.65b)

    Simplifying this equation:

    • 0.25a = 1.30b

    Dividing both sides by 0.05 to simplify further:

    • 5a = 26b

    Thus, the ratio b:a is:

    • b/a = 5/26

    Therefore, the ratio of the second number to the first number is 5:26 .

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