Math, asked by komalchauhan15, 5 months ago

The unit's digit of a two-digit number is three more than the tens digit. The number
obtained by reversing the digits is 27 more than the original number. Find the original
number

Answers

Answered by Anonymous
15

Given:

✰ The units digit of a two-digit number is three more than the tens digit.

✰ The number obtained by reversing the digits is 27 more than the original number.

To find:

✠ The original number

Solution:

Let the unit digit be X

Let the unit digit be XAnd digit in the 10s place be Y

Now, we know that the units digit of a two-digit number is three more than the tens digit.

  • Unit digit = 10s digit +3
  • X = Y + 3
  • X - Y = 3 ....①

The original number = 10Y + X

If it is reversed then the new number= 10X + y

According to question,

  • New number = Original number + 27
  • 10X + Y= 10Y + X + 27
  • 10X - X- 10Y + Y = 27
  • 9X - 9Y = 27
  • 9(X-Y) = 27
  • X- Y = 3 ...②

As we get same equations for above two conditions. They are dependents equations which have so many solutions .

In these some solutions are (two digit numbers):14,25,36,47,58

Check:-

14

  • Unit digit(4) = tens digit(1)+3
  • Original number(14)+27=reversed number(41)

25

  • Unit digit(5) = tens digit(2)+3
  • Original number(25)+27 = reversed number(52)

36

  • Unit digit(6) = tens digit(3)+3
  • Original number(36)+27 = reversed number (63)

47

  • Unit digit(7) = tens digit(4)+3
  • Original number(47)+27 = reversed number(74)

58

  • Unit digit(8) = tens digit(5)+3
  • Original number (58)+27 = reversed number(85)

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