The population of a city is 35000 On an increase of...

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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 ( 6 )

Shomsher John :

2 years ago

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
Shomsher John :

2 years ago

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
Rakesh Chodapaneedi :

3 years ago

Another short method plz..
Babun Padhiari :

6 years ago

tell other short method
Shivansh Srivastava :

7 years ago

please tell any short method
Ajay :

9 years ago

Tell me another method of this question