9 persons went to a hotel to have their meals. Eight of them spent Rs. 12 each…

Concept

For any group, the total of all values equals the number of members multiplied by their average: Total = n x Average. When one member's value is described relative to the group's average (for example, "Rs. 8 more than the average"), express that member's value in terms of the unknown average and solve the resulting equation.

Application

1. Let the average expenditure of all 9 persons be Rs. x.

2. By the definition of average, the total money spent by all 9 persons = 9 times x.

3. Eight persons spent Rs. 12 each, so their combined spending = 8 x 12 = Rs. 96.

4. The ninth person spent Rs. 8 more than the average, i.e., Rs. (x + 8).

5. The sum of all individual expenditures must equal the total: 96 + (x + 8) = 9x.

6. Simplify: x + 104 = 9x, so 8x = 104, giving x = 13.

7. Total money spent = 9 x 13 = Rs. 117.

Cross-check

Cross-check: with average Rs. 13, the eight persons contribute 8 x 12 = 96, and the ninth contributes 13 + 8 = 21; 96 + 21 = 117, which equals 9 x 13 = 117 -- consistent.

Hence, the total money spent by all nine persons is Rs. 117.

Reference (original worked image)