Question

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
​

Answer 1

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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