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In a party, one–fifth of the guests wanted cool drinks only. Out of the remaining, half of them liked coffee and two–thirds like tea. If 12 of the guests opted for both coffee and tea, how many guests had attended the party?

In a party, one–fifth of the guests wanted cool drinks only. Out of the remaining, half of them liked coffee and two–thirds like tea. If 12 of the guests opted for both coffee and tea, how many guests had attended the party? Correct Answer 90

Let total number of guests be x, then

Number of guests who wanted cool drinks = x × 1/5 = x/5

Remaining guests = x – x/5 = 4x/5

Number of guests who liked coffee = 4x/5 × 1/2 = 2x/5

Number of guests who liked tea = 4x/5 × 2/3 = 8x/15

Number of guests who liked tea and coffee both = 8x/15 – 2x/5 = (8x – 6x)/15 = 2x/15

According to the question

⇒ 2x/15 = 12

⇒ x = 12 × 15/2

⇒ x = 90

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