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
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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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