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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)

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

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Comments ( 4 )

  1. Rakesh Chodapaneedi
    Rakesh Chodapaneedi :
    4 months ago

    Another short method plz..

  2. Babun Padhiari
    Babun Padhiari :
    4 years ago

    tell other short method

  3. Shivansh Srivastava
    Shivansh Srivastava :
    4 years ago

    please tell any short method

  4. Ajay
    Ajay :
    6 years ago

    Tell me another method of this question

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