A village had provisions for 150 people for 45 days.

150×45=6750
10×150=1500
6750-1500=5250
150-25=125
5250÷125=42
Option C

Posted from my mobile device
_________________

\(125 : 150 :: 35 : x\)

\(x = 42\) , Answer must be (C)
_________________

Would have lasted 35 days if noone left so when 25 left its 35X(150/25) = 42

Can someone provide a more detailed explanation for this question please

Posted from GMAT ToolKit
_________________

SiddharthR hope this helps

_________________

That makes sense now. I was following the same approach but got lost somewhere. Thank you so much for clearing this out for me
_________________

Assume the provisions are 45 x 150 = 6750 boxes of food. Therefore, each person gets 45 boxes for 45 days, or 1 box per day. After 10 days, 150 x 10 = 1500 boxes are gone, and thus 6750 - 1500 = 5250 boxes are left. Since 25 people left after 10 days, we have 125 people left, and therefore, 125 boxes of food will be consumed per day. So 5250 boxes can last 5250/125 = 42 days.

Answer: C
_________________

(150*45-150*10)/125 = 42

You can solve this problem using proportional logic.

We have enough food to feed 150 people for 45 days. This is a steady amount X per day that we give to these 150 people so that it lasts 45 days.

10 days pass. 35 days remain in which each person is getting X food per day at a steady rate.

When the rate of food usage is held constant, the number of people we have to feed is inversely proportional to the amount of days we can feed them for.

Now, the 25 people leave. But we still are going to give out the same X units of food for day. Therefore, the number of days we can feed the fewer people should increase proportionally.



Decrease in the number of people we need to feed = - (25 / 150) = -(1/6)

When 2 quantities are inversely proportional, a decrease in quantity 1 of -(n) / (d + n) ————-> leads to an INCREASE in quantity 2 by + (n/d)


thus, a -(1/6) decrease in the number of people we have to feed ————> will lead to a +(1/5) increase in the number of days we can feed the remaining people for (assuming the rate of food usage is held constant)


(35 days) + (1/5) * (35 days) =

35 + 7 =

42 days

Posted from my mobile device