# 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)__

$$\eqalign{
& {\text{Let number of men in the population be }}x \cr
& {\text{Number of women}} = \left( {35000 - x} \right) \cr
& {\text{Increase in the number of men}} \cr
& = 6\% \,of\,x = \frac{{6x}}{{100}} \cr
& {\text{Increase in the number of women}} \cr
& = \left( {3500 - x} \right) \times \frac{4}{{100}} \cr
& {\text{Increase in whole population}} \cr
& = 36760 - 35000 = 1760 \cr
& {\text{Now}}, \cr
& \frac{{6x}}{{100}} + \left[ {\left( {35000 - x} \right) \times \frac{4}{{100}}} \right] = 1760 \cr
& \left[ {\left( {6x - 4x} \right) + 35000 \times \frac{4}{{100}}} \right] = 1760 \cr
& 2x + 35000 \times 4 = 1760 \times 100 \cr
& 2x = 176000 - 35000 \times 4 \cr
& x = 18000 \cr
& {\text{Number}}\,{\text{of}}\,{\text{men}} = 18000 \cr
& {\text{Number}}\,{\text{of}}\,{\text{women}} \cr
& = 35000 - 18000 \cr
& = 17000 \cr} $$ ## Join The Discussion

## Comments ( 4 )

Related Questions on Percentage

A. $$\frac{1}{4}$$

B. $$\frac{1}{3}$$

C. $$\frac{1}{2}$$

D. $$\frac{2}{3}$$

Another short method plz..

tell other short method

please tell any short method

Tell me another method of this question