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# Discussion

The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?

• A.34
• B.28
• C.12
• D.17

Any two digit number can be written as $$(10P + Q)$$, where $$P$$ is the digit in the tens place and $$Q$$ is the digit in the units place.
$$P + Q = 10$$ ----- (1)
$$(10Q + P) - (10P + Q) = 54$$
$$9(Q - P) = 54$$
$$(Q - P) = 6$$ ----- (2)
Solve (1) and (2) $$P = 2$$ and $$Q = 8$$
The required number is $$= 28$$

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