A village had provisions for 150 people for 45 days. After 10 days, 25 people left the village. How long will the provisions last at the same rate of usage for the remaining inhabitants?
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I set up the total provisions as 150*45 person-days. After 10 days, consumption is 150*10, so remaining is 150*35. Then with 125 people, days = (150*35)/125. Got 42, which is choice C. But wait, is it that simple? I feel like these problems usually have a twist.
Yes, that's exactly how I did it. The trick is to not fall for the trap of thinking the provisions last longer because fewer people, but you have to account for the 10 days already passed.
I initially thought the answer was 45, but then realized that after 10 days, the remaining provisions are only for 35 days at the original rate, so with fewer people it should be more than 35 but less than 45? Actually 42 makes sense.
Why is (B) 35 not the answer? I thought after 10 days, there are 35 days left for 150 people, so for 125 people it should be more than 35, but I'm not sure how to calculate. Can someone explain step by step?
Because the total food is fixed. If 150 people can eat for 35 days, then 125 people can eat for longer. The formula is (150*35)/125 = 42. So 35 is just the remaining days for the original group, not the new group.
This one was medium difficulty. I used the concept of 'man-days' and it worked. But I've seen similar problems where people join instead of leave, so you have to be careful. Here, 25 leave, so fewer people, provisions last longer. 42 is more than 35, which makes sense.
What it tests
Your ability to combine individual work rates, usually by working with the fraction of a job completed per unit of time.
Common trap
Adding the times instead of the rates, or forgetting to take the reciprocal when combining rates.