The population of a city is 35000. On an increase of 6% in the number of men and an increase of 4% in the number of women, the population would become 36760. What was the number of women initially?
A. 18000
B. 19000
C. 17000
D. 20000
Answer: Option C
Solution (By Examveda Team)
$$\eqalign{ & {\text{Let number of men in the population be }}x \cr & {\text{Number of women}} = \left( {35000 - x} \right) \cr & {\text{Increase in the number of men}} \cr & = 6\% \,of\,x = \frac{{6x}}{{100}} \cr & {\text{Increase in the number of women}} \cr & = \left( {3500 - x} \right) \times \frac{4}{{100}} \cr & {\text{Increase in whole population}} \cr & = 36760 - 35000 = 1760 \cr & {\text{Now}}, \cr & \frac{{6x}}{{100}} + \left[ {\left( {35000 - x} \right) \times \frac{4}{{100}}} \right] = 1760 \cr & \left[ {\left( {6x - 4x} \right) + 35000 \times \frac{4}{{100}}} \right] = 1760 \cr & 2x + 35000 \times 4 = 1760 \times 100 \cr & 2x = 176000 - 35000 \times 4 \cr & x = 18000 \cr & {\text{Number}}\,{\text{of}}\,{\text{men}} = 18000 \cr & {\text{Number}}\,{\text{of}}\,{\text{women}} \cr & = 35000 - 18000 \cr & = 17000 \cr} $$This Question Belongs to Arithmetic Ability >> Percentage
By Alligation method
Men 6% of 35000 = 2100
Female 4% of 35000 = 1400
Overall increase 10% ------> (36760-35000)
i.e = 1760
M. F
210 140
176
36 34 (original difference)
18 : 17 (ratio m:f)
Now, initially females = 17 /35 × 35000
Ans 17,000
By Alligation method
Men 6% of 35000 = 2100
Female 4% of 35000 = 1400
Overall increase 10% ------> (36760-35000)
i.e = 1760
M. F
210 140
176
36 34 (original difference)
18 : 17 (ratio m:f)
Now, initially females = 17 /35 × 35000
Ans 17,000
By applying Alligation
Male 6% of 35000 = 2100 (dearer value)
Female 4% of 35000 = 1400 (cheaper value)
Overall increase 10% -----> (36760-35000)
i.e = 1760
M F
210 140
176
36 34 (original difference)
18 : 17 (ratio m:f)
Now,
Initially Females = 17/35 × 35000
Ans 17,000
Let the initial number of men = M and women = W.
Given:
𝑀
+
𝑊
=
35000
(1)
M+W=35000(1)
After increase:
Men increase by 6% →
1.06
𝑀
1.06M
Women increase by 4% →
1.04
𝑊
1.04W
New total population:
1.06
𝑀
+
1.04
𝑊
=
36760
(2)
1.06M+1.04W=36760(2)
From (1):
𝑀
=
35000
−
𝑊
M=35000−W
Substitute into (2):
1.06
(
35000
−
𝑊
)
+
1.04
𝑊
=
36760
1.06(35000−W)+1.04W=36760
37100
−
1.06
𝑊
+
1.04
𝑊
=
36760
37100−1.06W+1.04W=36760
37100
−
0.02
𝑊
=
36760
37100−0.02W=36760
0.02
𝑊
=
340
0.02W=340
𝑊
=
340
0.02
=
17000
W=
0.02
340
=17000
Can be done with the Spider Method.
Let number of men in the population be x
Number of women = (35000−x)
Increase in the number of men = 6% of x
= 6x/100
Increase in the number of women = (35000−x) × 4/100
Increase in whole population = 36760 − 35000
= 1760
Now,
6x/100 + [(35000−x) × 4/100] = 1760
⇒ [(6x−4x) + 35000 × 4/100] = 1760
⇒ 2x + 35000 × 4 = 1760 × 100
⇒ 2x = 176000 − 35000 × 4
⇒ x = 18000
Number of men = 18000
Number of women = 35000 − 18000
= 17000
Let number of men in the population be x
Number of women = (35000−x)
Increase in the number of men = 6% of x
= 6x/100
Increase in the number of women = (35000−x) × 4/100
Increase in whole population = 36760 − 35000
= 1760
Now,
6x/100 + [(35000−x) × 4/100] = 1760
⇒ [(6x−4x) + 35000 × 4/100] = 1760
⇒ 2x + 35000 × 4 = 1760 × 100
⇒ 2x = 176000 − 35000 × 4
⇒ x = 18000
Number of men = 18000
Number of women = 35000 − 18000
= 17000
Another short method plz..
tell other short method
please tell any short method
Tell me another method of this question