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In the survey among girls at IIT Delhi, it was found that 46% preferred coffee and 15% preferred smoking. Also, 44% did not preferred coffee or smoking. If 55 girls like both coffee and smoking, then, find the total number of girls who participated in survey?

In the survey among girls at IIT Delhi, it was found that 46% preferred coffee and 15% preferred smoking. Also, 44% did not preferred coffee or smoking. If 55 girls like both coffee and smoking, then, find the total number of girls who participated in survey? Correct Answer 1100

Given:

Girls preferred coffee = 46%

Girls preferred smoking = 15%

Girls did not preferred coffee or smoking = 44%

Girls who preferred both coffee and smoking = 55

Concept:

Venn Diagram

Calculation:

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Suppose x% girls preferred both coffee and smoking.

Girls preferred only coffee = (46 – x)%

Girls preferred only smoking = (15 – x)%

Girls preferred neither coffee nor smoking = 44%

⇒ (46 – x)% + (15 – x)% + 44% + x% = 100%

⇒ 105% - x% = 100%

⇒ x = 5

∴ 5% → 55

⇒ 1% → 11

⇒ 100% → 1100

∴ The total number of girls who participated in survey = 1100

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