Question

sum of the digits of a two digit number is 5. when the digits are reversed the resulting number is greater than the original number by 27. find the number.​

Answer 1

let the digit in the units place be 'y' and the digit in the tens place be 'x'.

hence, the original number = 10x + y ... (i)

According to first condition:

x + y = 5

y = 5 - x ... (ii)

According to second condition:

$10y + x = 10x + y + 27 \\ 10y - y = 10x - x + 27 \\ \: \: \: \: \: \: \: \: \: \: 9y = 9x + 27 \\ \\ dividing \: throughout \: by \: 9 \: we \: get \ \\ \ \\ \: \: \: \: \: \: \: \: \: \: y = x + 27 \\ \: \: 5 - x = x + 27 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: (from \: ii) \\ 5 - 27 = x + x \\ \: \: \: \: \: \: \: \: 2x = - 22 \\ \: \: \: \: \: \: \: \: \: \: x = \frac{ - 22}{2} \\ = > \: x = - 11 \\ \\ substituting \: x = - 11 \: in \: (ii) \\ \\ \: \: \: \: \: \: \: \: y = 5 - ( - 11) = 5 + 11 \\ = > y = 16$

now, substituting x = -11 and y = 16 in (i)

original number = 10(-11) + 16 = -110 + 16

= -94

Hence, the number is -94.

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