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A student finds the average of ten 2 digits numbers. While copying numbers, by mistake, he writes in number with its digits interchanged. As a result his answer is 1.8 less than the correct answer. The difference of digits of the number, in which he made mistake is ?
Answer & Solution
Correct Answer:
Option
A
Let us consider by mistake he writes 10th number with its digits interchanged.
$$\therefore \frac{{10x + y - \left( {10y + x} \right)}}{{10}} = 18$$
(In this remaining nine numbers are same and they cancel out)
∴ 10x + y - 10y - x = 18
⇒ 9x - 9y = 18
⇒ x - y = 2
$$\therefore \frac{{10x + y - \left( {10y + x} \right)}}{{10}} = 18$$
(In this remaining nine numbers are same and they cancel out)
∴ 10x + y - 10y - x = 18
⇒ 9x - 9y = 18
⇒ x - y = 2
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