A group of men and women go to a restaurant. There are more men than women. If each person pays the bill according to what they ate, the average amount a man pays is Rs. 1300 and the average amount a woman pays is Rs. 1000. If, instead, the bill is shared equally among all the people, which of the following is a possible amount that each person pays?
Show Hint
- 1320
- 1135
- 1160
- 1100
The Correct Option is C
Solution and Explanation
Let \( m \) be the number of men and \( w \) be the number of women. Given \( m>w \). Average contribution of men = 1300. Average contribution of women = 1000. The overall average \( A \) (equal share amount) is: \[ A = \frac{1300m + 1000w}{m + w} \] Step 2: Determine the Range:
This average lies between 1000 and 1300. Since there are more men (\( m>w \)), the weight of the 1300 is higher. Therefore, the average must be closer to 1300 than to 1000. Midpoint = \( \frac{1300 + 1000}{2} = 1150 \). Because \( m>w \), the average \( A \) must be strictly greater than 1150. Range: \( 1150<A<1300 \). Step 3: Check Options:
(A) 1320: Impossible (cannot exceed max value 1300). (B) 1135: Less than 1150 (would imply more women). (C) 1160: Correct (between 1150 and 1300). (D) 1100: Less than 1150. Step 4: Final Answer:
The only possible amount is 1160.
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