5. The digit at ones place of a 2-digit number is four times the digit at tens place. The number obtained by reversing the digits exceeds the given number by 54. Find the given number.
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→y = 4x ---(i)
The the given number obtained by reversing the digits exceeds the given number by 54.
Reversed number = 10y + x
→ 10x + y + 54 = 10y + x
10x - x + y - 10y = 54
→ 9x - 9y = - 54
→ 9(x - y) = -54
→x - y = -6 --(ii)
Put the value of y in equation (ii)
→x - 4x = -6
- 3x = -6
x=2
Substitute the value of x in equation (i)
→y = 4x
→y = 4 x 2
→y=8
Hence,
Tens digit = x = 2 Ones digit=y=8
Therefore,
Original number = 10x + y = 28
Reversed number = 10y + x = 82
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