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Nine persons went to a hotel for taking their meals. Eight of them spent Rs.12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine. What was the total money spent by them?

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Rs. 120

Rs. 200

Rs. 117

Rs. 190

answer is C.

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Detailed Solution

Given that, eight people spent Rs 12 each for meal and nineth spent Rs.8 more than the average expenditure of all nine.
Mean can be calculated by using the formula,

x ¯ = ∑ x i n .

Here, n is number of observations,

x i

is value of observation.
Let

x ¯

be the average expenditure of nine.
As the ninth spend 8 more than the average expenditure, the amount spent by ninth person is

x ¯ + 8

.
Then,

⇒ x ¯ = 128 + x ¯ + 8 9 ⇒ x ¯ = 96 + x ¯ + 8 9 ⇒ x ¯ = 104 + x ¯ 9 ⇒ 9 x ¯ = 104 + x ¯ ⇒ x ¯ = 1048 ⇒ x ¯ = 13

The money spent by the ninth person.

x ¯ + 8 = 13 + 8 ⇒ 21

The money spent by all of them is,

128 + 21 = 96 + 21 ⇒ 117

Thus, the money spent by all of them is Rs.117.
Therefore, option (3) is correct.

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