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23%
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The population of a town is 5,500. If the number of males increases by 11% and the number of females increases by 20%, the total population becomes 6,330. What is the female population of the town?
A. 1800
B. 2000
C. 2500
D. 3000
E. 3500
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A. 1800
B. 2000
C. 2500
D. 3000
E. 3500
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.
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x + y = 5500.......(I)
1.11x + 1.2y = 6330 ......(ii)
Solve eqn (i) & (ii)
0.09y = 225
y = 2500
1.11x + 1.2y = 6330 ......(ii)
Solve eqn (i) & (ii)
0.09y = 225
y = 2500
IMO C.
M + F = 5500 & 1.11M + 1.2F = 6330, manipulate equation 1, hence F = 5500 - M
fyi I chose to manipulate equation 1 into "F =" because 1.2 is easier to deal with than 1.11 (would have to deal with 1.11M if I made equation 1 M=)
From here, we will have 1.11M + 6600 - 1.2M = 6330 ----> -0.09M = - 270 (Multiple both by 100)
Thus, -9M = -27000, divide both sides by -9M and M = 3000, plug into Equation 1 and F = 2500.
FYI. For the second to last step, I skipped the step of distributing 5500 - M in the equation but it should give you 6600 - 1.2M. Hope this helps
M + F = 5500 & 1.11M + 1.2F = 6330, manipulate equation 1, hence F = 5500 - M
fyi I chose to manipulate equation 1 into "F =" because 1.2 is easier to deal with than 1.11 (would have to deal with 1.11M if I made equation 1 M=)
From here, we will have 1.11M + 6600 - 1.2M = 6330 ----> -0.09M = - 270 (Multiple both by 100)
Thus, -9M = -27000, divide both sides by -9M and M = 3000, plug into Equation 1 and F = 2500.
FYI. For the second to last step, I skipped the step of distributing 5500 - M in the equation but it should give you 6600 - 1.2M. Hope this helps
Bunuel
M + F = 5500
1.11M + 1.2F = 6330
Solving the equations we get
1.11(5500-F) + 1.2F = 6330
0.09F =6330-6105 = 225
F = 2500
Answer: Option C
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Let male be X and female be Y
X+Y=5500
Y=5500-X...(1)
1.11X+1.2Y=6330- (2)
Solve the 2 equation
Y=2500
X+Y=5500
Y=5500-X...(1)
1.11X+1.2Y=6330- (2)
Solve the 2 equation
Y=2500
Bunuel
M+F= 5500
1.10M + 1.20F= 6,330
1.11(5500-F)+1.20F= 6330
111(5500-F)+120F=633000
610500-111F+120F=633000
9F=633000-610500
9F=22500
F=2500
Answer: C
1.10M + 1.20F= 6,330
1.11(5500-F)+1.20F= 6330
111(5500-F)+120F=633000
610500-111F+120F=633000
9F=633000-610500
9F=22500
F=2500
Answer: C
Bunuel
Let the number of Male be ‘m’. And the number of female be ‘f’.
5500 = m + f ————— eqn 1
6330 = 1.11 m + 1.20 f ————— eqn 2
From eqn 1, m = 5500 - f. Substitute it in eqn 2
6330 = 1.11 ( 5500 - f) +1.20 f
6330 = 6105 - 1.11 f + 1.20 f
225 = 0.09 f
f =2500. Option C
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