In a store, there was food sufficient to sustain a group of men for

Question

In a store, there was food sufficient to sustain a group of men for exactly 100 days. After 25 days of consumption, 8 more men joined the group, causing the food to last only for an additional 35 days. If each man consumed an equal amount of food daily, how many men were in the group initially?

A. 6
B. 7
C. 8
D. 15
E. 16

gmatophobia · Answer

Approach 1

Number of men in the group =  n

Amount of food consumed by each men per day =  x  units

Amount of food consumed by  n  men in  100  days =  100 * n * x  units

Food consumed in the first  25  days =  25 * n * x  units

Amount of food left =  100nx = 25nx = 75nx

Therefore  75nx  units of food was consumed by  (n+8)  men in  35  days

35(n+8)x = 75nx

280x + 35nx = 75nx

280x = 40nx

Cancelling  x  on both sides

n =\frac{ 280}{40} = 7

Approach 2

Because of the addition of 8 men, the food lasted only for 60 (i.e. 35 + 25) days instead of 100 days. So, the 8 men in the span of 35 days consumed the amount of food that  n  men would have consumed in 40 days

35 * 8 = 40 * n

7 * 5 * 8 = 40 * n

Dividing by 40 on both sides

n = 7

Option B

SarthakSharma8 · Answer

Let 'x' be the initial number of men
Food is sufficient for 100 days of their consumption so Food 'F' = x*100 -----(1)

Now,
For 25 days, Food consumed by 'x' men = 25*x
then 8 more men join the squad and the number of men becomes = x+8
now x+8 men eat for only 35 days so their Food consumption becomes = (x+8)*35
Total Food consumed becomes, 'F' = 25x +(x+8)35 -----(2)

Equating F from (1) and (2) :-

100x = 25x + 35x + 280
100x = 60x + 280
40x = 280
x = 7 ---- Answer

sayan640 · Answer

Given ,  Each man consumed an equal amount of food daily,  
Hence , 1 man in 1 day eats 1 unit of food.
Lets say , 'm' men was there in the group.

m men in 1 day consumes m units
m men in 25 days consumes 25m units
m in 100 days consume 100m units = total food

We can write ,
75m / (m+8) * 35 = 100m / (100*m)
Solving , m = 7

B is the ans.

In a store, there was food sufficient to sustain a group of men for

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