A number of friends decided to go on picnic and planned to spend Rs 108 on eatables. Three of them however did not turn up. As a consequence each one of the remaining had to contribute Rs 3 extra. The number of them who attended the picnic was:__________151296
Question
A number of friends decided to go on picnic and planned to spend Rs 108 on eatables. Three of them however did not turn up. As a consequence each one of the remaining had to contribute Rs 3 extra. The number of them who attended the picnic was:__________151296
Solution
Let's solve this problem step by step:
Step 1: Let's assume the number of friends who decided to go on the picnic is 'x'. So, each friend had to contribute Rs 108/x.
Step 2: But three of them did not turn up. So, the number of friends who actually went to the picnic is 'x-3'. Now, each of them had to contribute Rs 108/(x-3).
Step 3: According to the problem, the contribution of each friend increased by Rs 3 due to the absence of 3 friends. So, we can set up the equation as follows:
108/(x-3) = 108/x + 3
Step 4: Solve the equation:
Multiplying all terms by x(x-3) to clear the denominator, we get:
108x = 108(x-3) + 3x(x-3)
Simplify the equation:
108x = 108x - 324 + 3x^2 - 9x
Rearrange the terms:
3x^2 - 9x - 324 = 0
Divide the equation by 3:
x^2 - 3x - 108 = 0
Step 5: Factor the equation:
(x - 12)(x + 9) = 0
Step 6: Solve for x:
x = 12 or x = -9
Since the number of friends cannot be negative, we discard x = -9.
So, the number of friends who attended the picnic is x - 3 = 12 - 3 = 9.
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