some students planned a picnic. the total budget for hiring a bus was Rs1440.Later on 8 of these refused to go and instead paid their total share of money towards the fee of one ecnomically weaker student of their class,and thus the cost of each member who went for the picnic increased by Rs30.
1)how many students attended the picnic.2)how much money in total was paid towards the fee
Answers
Step-by-step explanation:
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Answer:
Step-by-step explanation:
Solution :-
Let x students planned the picnic.
Then,
(x - 8) students attended picnic.
Bus Charges = 1440
According to the Question,
⇒ 1440/(x - 8) - 1440/x = 30
⇒ 1/(x - 8) - 1/x = 30/1440
⇒ x - (x - 8)/(x - 8)x = 1/48
⇒ 8/(x² - 8x) = 1/48
⇒ x² - 8x = 384
⇒ x² - 8x - 384 = 0
⇒ x² - 24x + 16x - 384 = 0
⇒ x(x - 24) + 16(x - 24) = 0
⇒ x - 24 = 0 or x + 16 = 0
⇒ x = 24, - 16 (As x can't be negative)
⇒ x = 24
Hence, 24 students planned the picnic.
1. Number of students who attented the picnic = 24 - 8 = 16
2. Share of 24 students = Rs. 1440
Share of 8 students = Rs. (1440/24 × 8) = Rs. 480.
Hence, Rs. 480 paid towards the fee.
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