Q6 of 69 Page 6

The mean of 11 numbers is 35. If the mean of first 6 numbers is 32 and that of last 6 numbers is 37, find the 6th number.

Let the 6th number be x


Given that mean of 11 results = 35


∴ sum of 11 numbers = 11 × 35 = 385


Mean of the first 6 results = 32


Sum of first 6 numbers = 6 × 32 = 192


Mean of the last 6 results = 37


Sum of the last 6 results = 6 × 37 = 222


Therefore,


Sum of first 6 numbers + sum of last 6 numbers – 6th number = sum of 11 numbers


192 + 222 - x = 385


⇒ 414 – x = 385


⇒ x = 29


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