Question

Mr. Manmohan calculated the average of 10 'three digit numbers'. But due to mistake, he reversed the digits of a number and thus his average increased by 19.8. The difference between the unit digit and hundreds digit of that number is :

• A. 8
• B. 4
• C. 2
• D. can't be determined

Answer 1

The correct option is C 2

Remember $\frac{\begin{array}{c}abc\\ -cba\end{array}}{99(a-c)}$
where abc and cba are the three digit numbers and (a, c)$\ne$ 0
(First number = 100a + 10b + c; Second number = 100c + 10b + a.
So First bnumber - Second number = 99a - 99b = 99(a-b))
Again since the difference in average = 19.8
Therefore the difference in total = 19.8 $\times$ 10 = 198
Thus, 99 $\times$ (a - c) = 198
(a - c) = 2