The sum of the digits of the two of a two digit number is 7 if the number formed by reversing the digits is less than the original number by 27 find the original number.
Answers
Answer:
Step-by-step explanation:
Let the unit's digit be: x
Ten's digit: (7-x)
Original Number: 10(7-x) + x
Number formed by interchanging the digits: 10x + (7-x)
Difference between the Original and interchanged Number: 27
10(7-x) + x - (10x + 7-x) = 27
→70 - 10x + x - 10x - 7 + x = 27
→70 - 7 - 10x + x -10x + x = 27
→63 - 18x = 27
{Transposing 63 to RHS}
→-18x = 27 - 63
→-18x = -36
{Transposing -18 to RHS}
→x = -36/-18
→x = 2
Original Number: 10(7-x) + x
→ 70 - 10x + x
→ 70 - 9x
→ 70 - (9×2)
→ 70 - 18
→ 52
Checking the Conditions...
Original Number: 52
Interchanged Number: 25
Sum of digits: 5 + 2
→7
{First Condition is satisfied...}
Difference between Original and Interchanged Number: 52 - 25
→ 27
{Second Condition is also satisfied...}
Hence, the Original Number is 52.