Assume there to be some foodstuff that is sufficient for a team for $x$ number of days. After 20 days, 25% of team members happen to quit. It is observed that the remaining foodstuff is sufficient to feed the remaining members for another $x$ number of days. What is the value of $x$?
80
72
60
40
Answer is Right!
Answer is Wrong!
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UPSC CISF-AC-EXE – 2024
Let the initial number of team members be M.
The food is sufficient for M members for x days. Total food “units” can be represented as M * x.
After 20 days, the M members have consumed food for 20 days. The food consumed is M * 20 units.
The remaining food units = (Initial food) – (Food consumed) = M * x – M * 20 = M(x – 20).
After 20 days, 25% of the team members quit.
The remaining number of team members = M – 25% of M = M – 0.25M = 0.75M.
It is observed that the remaining food is sufficient to feed the remaining members (0.75M) for another x number of days.
So, the remaining food units can also be represented as (Remaining members) * (Number of additional days) = (0.75M) * x.
Equating the two expressions for the remaining food:
M(x – 20) = 0.75M * x
Since M represents the number of members, M must be greater than 0 (otherwise there is no team or food). We can divide both sides by M:
x – 20 = 0.75x
Now, solve for x:
x – 0.75x = 20
0.25x = 20
x = 20 / 0.25
x = 20 / (1/4)
x = 20 * 4
x = 80.