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Question

The population of a city increases by 10% in first year, increases by 20% in the second year and decreases by 10% in the third year. What would be the percentage increase/decrease in the population of the city after three years?

एक शहर की आबादी पहले साल 10% बढ़ती है, दूसरे साल 20% बढ़ती है और तीसरे साल 10% घटती है । तीन वर्षों के बाद शहर की आबादी में प्रतिशत में वृद्धि या कमी क्या होगी?

A
10% increase

10% वृद्धि
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B
20% increase

20% वृद्धि
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C
20% decrease

20% ह्रास
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D
18.8% increase

18.8% वृद्धि
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Solution

The correct option is D 18.8% increase

18.8% वृद्धि
Let the initial population of the city = z.
Percentage increase in the population after first year = 10%
So, the population after one year of city = z + 10% of z = 1.1z Percentage increase in the population after second years = 20% So, the population after second year = 1.1z + 20% of 1.1z = 1.1z × 1.2 = 1.32z
Percentage decrease in the population after third year = 10%. Population after third year = 1.32z – 10% of 1.32z = 1.32z × 0.90 = 1.188z
So, required percentage increase = (1.188zzz)×100=18.8%
Thus, the population of city will increase by 18.8% in the three years.
Hence, option (d) is the correct answer.

माना कि शहर की आरंभिक जनसंख्या = z
प्रथम वर्ष के पश्चात् शहर की जनसंख्या में प्रतिशत वृद्धि = 10% इसलिए, प्रथम वर्ष के पश्चात् शहर की जनसंख्या = z + 10% of z = 1.1z
द्वितीय वर्ष के पश्चात् जनसंख्या में प्रतिशत वृद्धि = 20%
इसलिए, द्वितीय वर्ष के पश्चात् जनसंख्या = 1.1z + 1.1z का 20% = 1.1z × 1.2 = 1.32z
तृतीय वर्ष के पश्चात् जनसंख्या में प्रतिशत ह्रास = 10%
तृतीय वर्ष के पश्चात् जनसंख्या = 1.32z – 10% of 1.32z = 1.32z × 0.90 = 1.188z
इसलिए, वांछित प्रतिशत वृद्धि = 0.188 × 100 = 18.8%
​​​​​​​इस प्रकार, तीन वर्षों में शहर की जनसंख्या 18.8% बढ़ेगी। इसलिए, विकल्प (d) सही उत्तर है।

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