The sum of the digits of a two digit number is 5 if the digits is reversed,the new number decreased by 27 find the number
Answers
Answer:
Step-by-step explanation:
Answer:
Original Number: 41.
Step-by-step explanation:
Let the digit in the unit's place be: x.
Sum of digits: 5.
Digit in ten's place: (5-x).
Original Number: 10(5-x) + x.
Number formed by revering the digits: 10x + (5-x).
Difference between the numbers: 27.
Therefore, we get,
→[10(5-x) + x] - 27 = 10x + (5-x)
→50 - 10x + x - 27 = 10x + 5 - x
→23 - 9x = 9x + 5
{Transposing -9x to RHS and 5 to RHS...}
→23 - 5 = 9x + 9x
→18 = 18x
{Transposing 18 to LHS...}
→18/18 = x
→1 = x
→x = 1
Original Number: 10(5-x) + x →10(5-1) + 1 →10(4) + 1 → 40+1 → 41.
Interchanged Number: 10x + (5-x) → 10(1)+(5-1) → 10+4 → 14.
Checking the Solution...
Original Number: 41.
Sum of digits: 4+1 → 5.
Given sum of digits: 5.
5 = 5. {First Condition Satisfied...}
Interchanged Number: 14.
Difference between Original and Interchanged Number: 41 - 14 → 27.
Given Difference: 27.
27 = 27. {Second Condition Satisfied...}
Hence, the Required Number is 41.
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