The total population of a town is 2800, where the number of males is 720 more than that of females. If the number of males reduces by 40% and that of females increases by 20%, then find the new population of the town?
Answer (2)
After calculating the number of males and females in the town, we find that there are 1760 males and 1040 females. After a 40% reduction in males and a 20% increase in females, the new total population becomes 2304. Therefore, the final answer to the question is that the new population of the town is 2304.
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To solve this problem, we need to find out the initial number of males and females in the town and then calculate the change in population after the specified percentage changes in their numbers.
Let's define the variables:
Let M represent the initial number of males.
Let F represent the initial number of females.
According to the problem:
M + F = 2800 (The total population)
M = F + 720 (The number of males is 720 more than females)
Using the second equation, we can substitute for M in the first equation:
( F + 720 ) + F = 2800
Simplifying, we get:
2 F + 720 = 2800
Subtract 720 from both sides:
2 F = 2080
Divide both sides by 2 to solve for F :
F = 1040
Now, substitute F = 1040 back into the equation for M :
M = 1040 + 720 = 1760
So, initially, there were 1760 males and 1040 females.
Next, we calculate the changes:
The number of males is reduced by 40%: Reduced males = 1760 − ( 0.4 × 1760 ) = 1760 − 704 = 1056
The number of females increases by 20%: Increased females = 1040 + ( 0.2 × 1040 ) = 1040 + 208 = 1248
Now, let's find the new population:
New population = 1056 + 1248 = 2304
Therefore, after the changes, the new population of the town is 2304.
