The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly added. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
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$40.2$
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$40.4$
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$40.6$
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$40.8$
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$None of these$
A
Correct answer
Explanation
Original sum = 10 * 40.2 = 402. First error: added number that was 18 greater than actual. This increased sum by 18. Second error: added 13 instead of 31. This decreased sum by 31-13 = 18. Net change in sum: +18 - 18 = 0. Therefore correct sum = 402, and correct average = 402/10 = 40.2. The errors cancel out exactly.