Some students planned a picnic. The total budget for hiring a bus was Rs. 1440. Later on, eight of these refused to go and instead paid their total share of money towards the fee of one economically weaker student of their class, and thus, the cost for each member who went for picnic, increased by Rs. 30.
(i) How many students attended the picnic?
(ii) How much money in total was paid towards the fee? Which value is reflected in this question?

Explanation

Let x students planned the picnic.
Then, `(x-8)` students attended the picnic.
Total bus charges `= Rs. 1440.`
`:." "(1440)/((x-8))=(1440)/(x)=30`
`implies" "(1)/((x-8))-(1)/(x)=(30)/(1440)implies(x-(x-8))/((x-8)x)=(1)/(48)`
`implies" "(8)/((x^(2)-8x))=(1)/(48)impliesx^(2)-8x=384" "["by cross multiplication"]`
`implies" "x^(2)-8x-384=0impliesx^(2)-24x+16x384=0`
`implies" "x(x-24)+16(x-24)=0implies(x-24)(x+16)=0`
`implies" "x-24=0" or "x+16=0impliesx=24" or "x=-16`
`implies" "x=24" "[because" number of students cannot be negative"]`
Thus, 24 students planned the picnic.
(i) Number of tudents who attended the picnic `=(24-8)=16.`
(ii) Share of 24 students `=Rs. 1440`
Share of 8 students `=Rs. ((1440)/(24)xx8)=Rs. 480.`
`:." "`money paic towareds the fee `=Rs. 480.`
The value reflected in the given question is 'charity'.