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When 10% of the inhabitants of a village died of cholera, a panic set in, during which 25% of the remaining inhabitants left the village. The population then reduced to 4050. Find the number of original inhabitants.
7000
5000
8000
6000
6000
To solve this problem, we calculate the remaining population sequentially. After 10% of the original population P dies, 90% remain; subsequently, 25% of this remainder leaves, leaving 75% of the 90% population, which equals 4050.
To solve this problem, we calculate the remaining population sequentially. After 10% of the original population P dies, 90% remain; subsequently, 25% of this remainder leaves, leaving 75% of the 90% population, which equals 4050.
Think of this like a decaying radioactive isotope; you are removing a fraction of the current amount, not a fixed percentage of the initial amount every time.
PfinalтАЛ=PinitialтАЛ├Ч(1тИТ100r1тАЛтАЛ)├Ч(1тИТ100r2тАЛтАЛ) тАФ Formula for successive percentage changes
The principle involves successive percentage reduction. If the initial population is P, the population after cholera is P├Ч(1тИТ0.10)=0.9P. After 25% of this leaves, the remaining population is (0.9P)├Ч(1тИТ0.25)=0.9P├Ч0.75. Setting this to 4050 allows us to solve for P.
Successive reductions are multiplicative, not additive.
Order of reduction does not change the final result if percentages remain consistent.
The remaining percentage after a 10% loss is 90% and after a 25% loss is 75%.
Provides a clear method for calculating chain reactions or population dynamics.
Requires careful identification of the 'remaining' base for each step.
Calculating interest rates
Determining half-life and decay in radioactive substances
Calculation: P├Ч0.9├Ч0.75=4050тЗТP├Ч0.675=4050тЗТP=6000.
Wrong options: If one incorrectly adds 10%+25%=35%, they would calculate 65% of P, leading to an incorrect result.
D is correct тАФ The original population is found by solving P├Ч0.9├Ч0.75=4050, resulting in 6000.
In competitive exams, always multiply the fractions directly: P├Ч109тАЛ├Ч43тАЛ=4050 to simplify calculations rapidly.
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