The average of 24 numbers is 43. If we subtract a number 'M' from each number, then the average becomes 38. What was the value of M?
Answer & explanation
Correct answer: option 2
Average of 24 numbers = $\frac{Sum\;of\;numbers}{24}$
⇒ $\frac{Sum\;of\;numbers}{24}$ = 43
⇒ Sum of numbers = 43 x 24
If 'M' is subtracted from each number, total of 43M is subtracted from the sum, such that
New sum of the numbers = 43 x 24 - 24M = 24(43 - M)
New average = $\frac{24(43-M)}{24}$
⇒ $\frac{24(43-M)}{24}$ = 38
⇒ 43 - M = 38
Thus, M = 5