Question

Answer the question step by step

Answer 1

Let the Number of Boys in the Tea party be : B

Let the Number of Girls in the Tea party be : G

Given : Nine friends had a Tea party

$:\implies$  Number of Boys + Number of Girls should be equal to 9

$:\implies$  B + G = 9

$:\implies$  G = 9 - B

Given : Cost per cup of Coffee in rupees is numerically 2 less than the number of Girls

$:\implies$  Cost per cup of Coffee = (G - 2) rupees

Given : All Boys took only Coffee

$:\implies$  Total Number of Boys = Total Number of Coffee's

$:\implies$  Total number of Coffee's = B

$:\implies$  Total Expenses of the Boys on Coffee = B(G - 2) rupees

Given : Cost per cup of Tea in rupees is numerically 2 less than the number of Boys

$:\implies$  Cost per cup of Tea = (B - 2) rupees

Given : All Girls took only Tea

$:\implies$  Total Number of Girls = Total Number of Tea's

$:\implies$  Total number of Tea's = 9 - B

$:\implies$  Total Expenses of the Girls on Tea = (B - 2)(9 - B) rupees

Given - Ratio of the total expenses of the Boys and Girls is 5 : 6

$\mathsf{:\implies \dfrac{B(G - 2)}{(B - 2)(9 - B)} = \dfrac{5}{6}}$

$\mathsf{:\implies \dfrac{B(9 - B - 2)}{(B - 2)(9 - B)} = \dfrac{5}{6}}$

$\mathsf{:\implies \dfrac{B(7 - B)}{(B - 2)(9 - B)} = \dfrac{5}{6}}$

$:\implies$  6B(7 - B) = 5(B - 2)(9 - B)

$:\implies$  42B - 6B² = 5[9B - B² - 18 + 2B]

$:\implies$  42B - 6B² = 5[-B² + 11B - 18]

$:\implies$  42B - 6B² = -5B² + 55B - 90

$:\implies$  6B² - 5B² + 55B - 42B - 90 = 0

$:\implies$  B² + 13B - 90 = 0

$:\implies$  B² + 18B - 5B - 90 = 0

$:\implies$  B(B + 18) - 5(B + 18) = 0

$:\implies$  (B + 18)(B - 5) = 0

$:\implies$  B = -18  (or)  B = 5

As Number of Boys in the Tea Party cannot be a Negative Number

$:\implies$  B ≠ -18

$:\implies$  B = 5

$:\implies$  Total Number of Boys in the Tea party (B) = 5

$:\implies$  Total Number of Girls in the Tea party (G) = 4

We found that : Cost of each Coffee = (G - 2) rupees

$:\implies$  Cost of each Coffee = (4 - 2) Rs.

$:\implies$  Cost of each Coffee = 2 Rs.

Answer : Option (1)

Answer 2

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