Some students planned a picnic The …

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