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Home Aptitude Linear Equation See What Others Are Saying!
  • Question
  • The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54. If the sum of the two-digit number is 10, then what is the original number?


  • Options
  • A. 28
  • B. 39
  • C. 82
  • D. cannot be determined

  • Correct Answer
  • 82 

    Explanation

    Let us assume the digits of the original number are unit's digit a and ten's digit b.
    The Original Number will be 10a + b.
    After interchanging the digits the new number will be 10b + a.
    According to question,
    The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54.
    New Number = Original Number - 54
    10b + a = 10a + b - 54
    ? 10b + a - 10a - b = -54
    ? 9b - 9a = -54
    ? a - b = 6....................................(1)
    Again according to question,
    Sum of the digits of original number = 10
    a + b = 10..................................................(2)
    Add the equation (1) and (2), we will get
    a - b + a + b = 10 + 6
    2a = 16
    a = 8
    Put the value of a in Equation (2) , we will get
    8 + b = 10
    b = 10 - 8
    b = 2
    Put the value of a and b for original number, we will get
    10a + b = 10 x 8 + 2 = 80 + 2 = 82


  • More questions

    • 1. 
      Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?

    • Options
    • A. 18 days
    • B. 21 days
    • C. 3 days
    • D. 6 days
    • Discuss
    • 2. 
      750.0003 ÷ 19.999 =?

    • Options
    • A. 49
    • B. 18
    • C. 22
    • D. 38
    • Discuss
    • 3. 
      105, 85, 60, 30, 0, - 45, - 90?

    • Options
    • A. 0
    • B. 85
    • C. -45
    • D. 60
    • Discuss
    • 4. 
      Let A = {1, 2, {3, 4}, 5}. Which of the following statements is true?

    • Options
    • A. {3, 4} ? A
    • B. {3, 4} ? A
    • C. 1 ? A
    • D. {1, 2, 5} ? A
    • Discuss
    • 5. 
      Two vessels A and B contains milk and water mixed in the ratio 5 : 3 and 2 : 3. When these mixtures are mixed to form a new mixture containing half milk and half water, they must be taken in the ratio ?

    • Options
    • A. 2 : 5
    • B. 3 : 5
    • C. 4 : 5
    • D. 7 : 3
    • Discuss
    • 6. 
      1, 2, 4, 8, 16, 32, 64, (...), 256?

    • Options
    • A. 148
    • B. 128
    • C. 154
    • D. 164
    • Discuss
    • 7. 
      A tree is 12 m tall and casts an an 8 m long shadow. At the same time, a flag pole caste a 100 m long shadow. How long is the flag pole?

    • Options
    • A. 150 m
    • B. 200 m
    • C. 125 m
    • D. 115 m
    • Discuss
    • 8. 
      8% of 96 =? of 1/25

    • Options
    • A. 19.2
    • B. 7.68
    • C. 1.92
    • D. None of these
    • Discuss
    • 9. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

    • Options
    • A. Rs. 35
    • B. Rs. 245
    • C. Rs. 350
    • D. Cannot be determined
    • E. None of these
    • Discuss
    • 10. 
      If the hands of a clock coincide in every 65 minutes (true time), in 24 hours the clock will gain:

    • Options
    • A. 10 10 minutes. 143
    • B. 9 12 minutes. 143
    • C. 11 12 minutes. 143
    • D. 12 10 minutes. 143
    • Discuss


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