Multiple choice

A group of men and women go to a restaurant. There are more men than women. If each person pays the bill based on what they ate, the average amount paid by a man is Rs. 1,300 and by a woman is Rs. 1,000. If instead the total bill is split equally among all the people, which of the following could be the amount each person pays?

  1. Rs. 1,320

  2. Rs. 1,100

  3. Rs. 1,160

  4. Rs. 1,135
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M be number of men and W be number of women. M > W. Average = (1300M + 1000W) / (M+W). Since M > W, the average must be closer to 1300 than 1000. The range is 1000 < Avg < 1300. Specifically, if M=2, W=1, Avg = 3600/3 = 1200. If M=3, W=2, Avg = 5900/5 = 1180. 1160 is a possible value.

AI explanation

When a total bill is split equally, the overall average paid must lie strictly between the lowest individual average of Rs 1000 and the highest individual average of Rs 1300. Since there are more men than women, the combined average must be weighted closer to the men's average, meaning it must be greater than the exact middle of 1150. Looking at the options, Rs 1320 is impossible because it exceeds 1300, Rs 1100 is impossible because it is below 1150, and Rs 1135 is also below 1150. The only possible amount greater than 1150 is Rs 1160.

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