A village had provisions for 150 people for 45 days.

Question

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?

(A) 25

(B) 35

(C) 42

(D) 45

(E) 60

Mohammadmo · Accepted Answer

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

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ScottTargetTestPrep · Answer

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

Abhishek009 · Answer

125 : 150 :: 35 : x

x = 42  , Answer must be (C)

PinakiRDas · Answer

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

SiddharthR · Answer

Can someone provide a more detailed explanation for this question please

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bacseialex · Answer

SiddharthR  hope this helps

rvgmat12 · Answer

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

Fdambro294 · Answer

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

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AkRaGMAT99 · Answer

w1/(m1*r1*d1) = w2/(m2*r2*d2)
Where w: is work done
m: is number of people
r: rate of work
d: number of days

In our case, 
w is constant (finishing the food)
r is constant (same rate)
m1 = 150, m2= 125
d1 is 35 (given the people would finish in the food at the constant days in the  remaining  35 days)
d2 is what we need to find

So, we get d2 = 150*35/125 = 2

sunshineeee · Answer

Provisions = food supply

Total food supply available: 150 people x 45 days = 4500+2250 = 6750

Food supply spent in 10 days: 150 people x 10 days = 1500
Left: 6750 - 1500 = 5250

Food supply left per heads-> 5250 / (150-25) = 5250 / 125 = 42 foods/people (answer C)

A village had provisions for 150 people for 45 days.

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A village had provisions for 150 people for 45 days.

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