Question: The population of the village is 5500. If the number of males increase by 11% and the number of females increase by 20%, then the population becomes 6330. Find the population of females in the town.

1. 2500
2. 3000
3. 2000
4. 3500
5. 1800

Correct Answer: A
Solution and Explanation:
Approach Solution 1:
I. Algebraic …
Let the number be m and f
So m+f=5500.......(I)
1.11m+1.2f=6330..(ii)
Multiply (I) by 1.2 and subtract from (ii)
1.2m+1.2f-(1.11m+1.2f)=6600-6330
0.09m=270......m=3000
f=5500-3000= 2500

II... Weighted average
If all were male increase would be (1.11-1)*5500=605
If all were females, increase would be (1.2-1)*5500=1100
Combined the increase was 6330-5500=830
So 605...830...1100
Ratio of female to total = (830-605)/(1100-605)=225/495=5/11
So females =5500*5/11= 2500

Approach Solution 2:
x is population of male
Therefore, (5500-x is the population of female
x*111/100+(5500-x)*120/100= 6330
On calculating we get x = 3000

So the female population = 2500.

Approach Solution 3:
Given:
The population of a village is 5500
Increase in number of males 11%

Increase in number of females 20%
Total population= 6330

Calculation:
Let x be the population of females in the village
Now, as per the question
The number of males in the village= (5500-x)

Now, as per the question
(5500-x)*111%+x*120%= 6330
= 111(5500-x)*120x= 6330*100
= 111*5500-111x+120x= 6330*100
9x= 633000-610500
= 9x= 22500
= x= 2500

Therefore, the population of females in the town is 2500.

“The population of the village is 5500. If the number of males increase”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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