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Some students planned a picnic The …

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Some students planned a picnic The total budget for hiring a bus was rupee 1440 later on 8 of those 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 of each member who went for picnic increased by rupee 30. How many students attended the picnic and how much money in total was paid towards the fee?
  • 1 answers

Sia ? 6 years, 6 months ago

Let x students planned the picnic.
Then, (x - 8) students attended the picnic.
Total bus charges = Rs. 1440
{tex}\therefore \quad \frac { 1440 } { ( x - 8 ) } - \frac { 1440 } { x } = 30{/tex}
{tex}\Rightarrow \frac { 1 } { ( x - 8 ) } - \frac { 1 } { x } = \frac { 30 } { 1440 } \Rightarrow \frac { x - ( x - 8 ) } { ( x - 8 ) x } = \frac { 1 } { 48 }{/tex}
{tex}\Rightarrow \quad \frac { 8 } { \left( x ^ { 2 } - 8 x \right) } = \frac { 1 } { 48 } \Rightarrow{/tex} x2 - 8x = 384 [ by cross multiplication]
{tex}\Rightarrow{/tex} x2 - 8x - 384 = 0 {tex}\Rightarrow{/tex} x2 - 24x + 16x - 384 = 0
{tex}\Rightarrow{/tex} x(x - 24) + 16(x - 24) = 0 {tex}\Rightarrow{/tex} (x - 24)(x + 16) = 0
{tex}\Rightarrow{/tex} x - 24 = 0 or x + 16 = 0 {tex}\Rightarrow{/tex} x = 24 or x = -16
{tex}\Rightarrow{/tex} x = 24 [{tex}\because{/tex} number of students cannot be negative]
Thus, 24 students planned the picnic.

  1. Number of students who attended the picnic = (24 - 8) = 16
  2. Share of 24 students = Rs. 1440

Share of 8 students = Rs. {tex}\left( \frac { 1440 } { 24 } \times 8 \right){/tex} = Rs. 480
{tex}\therefore{/tex} money paid towards the fee = Rs. 480

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