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  • Question

  • In a two-digit number, the digit at the unit's place is 1 less than twice the digit at the ten's place. If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is


  • Options
  • A. 47
  • B. 59
  • C. 23
  • D. 35

  • Correct Answer
  • 47 

    Explanation

    let us assume the ten's digit number be x and unit's place digit be y.
    Then two digit Original Number = 10x + y
    According to question ? y = 2x - 1 ................(1)
    When digits are interchanged then new number = 10y + x
    If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20,
    New Number - Original Number = Original number - 20
    ? 10y + x - (10x + y) = 10x + y - 20
    ? 10y + x - 10x - y - 10x - y = - 20
    ? 8y - 19x = - 20
    ? 19x - 8y = 20 ...................(2)
    Put the value of y from equation (1) in above equation (2).
    ? 19x - 8(2x - 1) = 20
    ? 19x - 16x - 8 = 20
    ? 7x = 20 + 8
    ? 7x = 28
    ? x = 28/7
    ? x = 4
    Put the value of y in equation (1)
    From (i) y = 2 x 4 -1 = y = 7
    ? original number = 10x + y =10 x 4 + 7 = 47.

    • More questions

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      A can complete a piece of work in 10 days, while B alone can complete it in 15 days. They work together for 5 days and rest of the work is done by C in 2 days. If they receive $ 450 for the whole work, how should they divide the money?

    • Options
    • A. $250, $100, $100
    • B. $225, $150, $75
    • C. $200, $150, $100
    • D. $175, $175, $100
      • Discuss
    • 2. 
      The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is :

    • Options
    • A. 50 ?3 m
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    • C. 75 ?3 m
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      • Discuss
    • 3. 
      If 30% of A = 20 % of B, then find the value of A : B?

    • Options
    • A. 1 : 3
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    • C. 3 : 1
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      • Discuss
    • 4. 80 litre mixture of milk and water contains 10% milk. How much milk (in litres) must be added to make water percentage in the mixture as 80%?

    • Options
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      • Discuss
    • 5. 
      If log 5 (x 2 + x) - log 5 x = 2 then the value of x is?

    • Options
    • A. 24
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    • 6. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

    • Options
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      • Discuss
    • 7. 
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    • Options
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    • 9. 
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    • Options
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    • 10. 
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    • Options
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