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July 23 2017
Question 1. A three digit number consists of 9, 5 and one more number. When these digits are reversed and then subtracted from the original number the answer yielded will be consisting of same digits arranged yet in different order. What is the other digit?
Answer

Let the digit unknown be n.

The given number is then, 900+50+n = 950+n

When reserved, the new number is 100n+50+9 = 59+100n.

subtracting these two numbers we get 891 - 99n

the digit can be arranged in 3 ways or 6 ways.

we already investigated 2 of these ways.

we can now try one of the remaining 4 ways. one of these is n95

100n+90+5 = 891 - 99n

or 199n = 796

so n =4

thus the unknown digit is 4

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