Question

Heya...!! ✋

Here's the question ↓


Q.) By 8 pm all the party guests had arrived . By 9 pm a third of them had departed . By 10 pm a third of those remaining had also departed . By 11 pm the same happened again and a third of those remaining had also departed. After this only 8 guest still remained at the party . How many guest were originally at thr party at 8 pm ??






❌ Wrong answers will be deleted on the spot. ❌

Answer 1

Let the number guest be x
At 9PM 1/3 departed = x/3
Guests remained = x - x /3
=> 2x/3
At 10PM 1/3 departed = 2x/9
Guests remained = 2x /3 - 2x /9
=> 4x/9
At 11PM 1/3 guests departed = 4x /27
Guests remained = 4x /9 - 4x /27
=>8x /27
8 guests are remained = 8x /27
8x/27 = 8
8x = 8 × 27
x = 8 × 27/8
x = 27
Number of guests are 27.

Answer 2

Hello ,

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Suppose total number of guests arrived are x.

●At 8 pm, total number guests = x

●At 9 pm, total number of guests =

$x - \frac{x}{3} = \frac{2x}{3}$

●At 10 pm, total number of guests = 

$\frac{2x}{3} - \frac{2x}{3} \times \frac{1}{3 } = \frac{2x}{3} - \frac{2x}{9} = \frac{4x}{9}$

●At 11 pm, total number of guests = 

$\frac{4x}{9} - \frac{4x}{9} \times \frac{1}{3} = \frac{4x}{9} - \frac{4x}{27} = \frac{8x}{27}$

Now according to the question only 8 guests still remained, so we have;

$\frac{8x}{27} = 8 \\ \\ = > x = 27$


☆☆☆Therefore total number of guests arrived were 27. (Ans.)


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Hope it satisfied my answer

# Nikky