Nine persons went to a hotel for taking their meals. Eight of them spent Rs. 12 each of their meals and the ninth spent Rs. 8 more than the average expending of all the nine. Total money spent by them was?
Question
Nine persons went to a hotel for taking their meals. Eight of them spent Rs. 12 each of their meals and the ninth spent Rs. 8 more than the average expending of all the nine. Total money spent by them was?
Solution
Step 1: Calculate the total amount spent by the first eight people. Since each of them spent Rs. 12, the total amount is 8 * 12 = Rs. 96.
Step 2: Let's denote the average expenditure of all nine people as 'A'. According to the problem, the ninth person spent Rs. 8 more than the average. So, the ninth person spent A + 8 Rs.
Step 3: The total expenditure of all nine people is the sum of the expenditures of the first eight people and the ninth person. So, the total expenditure is 96 + A + 8.
Step 4: But we also know from the problem that the total expenditure is the average expenditure times the number of people. So, the total expenditure is also 9 * A.
Step 5: Now we can set up the equation 96 + A + 8 = 9 * A and solve for A.
Step 6: Simplify the equation to 104 = 9A.
Step 7: Solve for A by dividing both sides of the equation by 9. A = 104 / 9 = Rs. 11.56 (approximately).
Step 8: Therefore, the total money spent by them was 9 * A = 9 * 11.56 = Rs. 104.04.
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