Multiple choice

In a science experiment which was done 10 times, an intern calculated the average of all the readings and he noticed that all the readings are in 2 digits. After cross checking, his professor found out that reading digits are interchanged due to which average is 1.8 less than the exact value. Calculate the difference of the digits of the numbers in which he made a mistake.

  1. 2

  2. 3

  3. 4

  4. 6
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A Correct answer
Explanation

Let the two-digit number be 10x + y. Interchanging digits gives 10y + x. The difference is (10x + y) - (10y + x) = 9(x - y). Since the average of 10 readings changed by 1.8, the total sum changed by 10 * 1.8 = 18. Thus, 9(x - y) = 18, which means x - y = 2.

AI explanation

When a two digit number with tens digit a and units digit b is reversed, the value changes by the quantity 9 times (a minus b). The total decrease across all 10 readings is the average drop of 1.8 multiplied by 10, which equals 18. Setting the change for the single reversed number to match this total error gives the equation 9 times (a minus b) equals 18. Solving this shows the difference between the digits (a minus b) is 2.

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