a) 18000
b) 19000
c) 17000
d) 20000

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