Initial population of a town was 8000 people

Question

Initial population of a town was 8000 people. In one year male population increased by 10% and female population increased by 8%. The total increase in population was 9%. How many males were there initially ?

A. 3600
B. 4000
C. 5000
D. 6000
E. 7200

A. 3600
B. 4000
C. 5000
D. 6000
E. 7200

agarwalankur · Accepted Answer

This is a tricky question which could be solved in 30 secs

Look at the percentages: 10% population growth in men and 8% in women. Net Weighted average growth is 9% which is possible if and only if Men:Female ratio is 1:1. Hence both men and women are 4000 each.

Ans: 4000. MarkB

mbamisfit · Answer

assume male population = x then female = 8000 - x
New male pop = 1.1*x, New female pop = 1.08*(8000-x), new total pop = 1.09*8000

1.09*8000 = 1.1*x + 1.08*(8000-x)
> 8720 - 8640 = 0.02x 
>x = 4000
> Ans = B

vanshi2301 · Answer

Let males in the initial population be x.
Then females= 8000-x
Population increase= 9% of 8000= 720
Increase in males= 10% of x
Increase in females= 8% of (8000-x)

10% of x + 8% of (8000-x) = 720
Solving this, we will get, x=4000

Answer: B

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aggvipul · Answer

Explanation (rather concept):
Its a question of Mixtures and Alligations

1. Find out the %tage difference between the total and individual
therefore, difference for Men = 1 (10-9)
difference for Women = 1 (9-8)

2. Take the ratio of the differences, this ratio would represent the initial Men:Women population ratio = 1:1
hence, Men initially= 1/2 of Total initial population = 4000

fireagablast · Answer

yikes yeah the solution is incredibly simple. No need to really even calculate anything.

10-9:9-8
1:1 --> ratio of men to women
8000*1/2 = 4000

rajatchopra1994 · Answer

Explanation:

let male = x, females = y.
(x+y=8000)*1.1 ---- 1 
in one year , population has increased by 9% and male by 10% , Female by 8%.
1.1x + 1.08y = 1.09x8000
1.1x + 1.08y = 8720 --- 2
Solving 1 & 2
.02y = 80
y=4000, x=4000
IMO-B

ScottTargetTestPrep · Answer

Solution:

Since 9% is exactly the average of 10% and 8%, it must be true there were an equal number of men as women. Therefore, there were 8000/2 = 4000 men initially.

Answer: B

Prakruti_Patil · Answer

I solved it this way, but then assumed 4000 was 110% the male population.. how do we know it is original population and not the increased one?

KhayatiK · Answer

i started w this approach , got the 1:1 but then was unsure if this 1:1 could be applied to the "before increase population" as the 1:1 was a derivative of increased population indicating , possibly, the ratios post increase could have changed. am i missing some logic here ?

Initial population of a town was 8000 people

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Initial population of a town was 8000 people

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