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19 Sep 2023, 08:46
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Difficulty:
55%
(hard)
Question Stats:
69% (02:39) correct
31%
(02:45)
wrong
based on 182
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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
A. 6
B. 7
C. 8
D. 15
E. 16
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19 Sep 2023, 10:46
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Bunuel
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
16 Oct 2023, 19:46
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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
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
