Given x and yare inversely proportional
xy = constant
wheny = 35 and constant = 7; x x 35 = 7

\(x=\cfrac { 1 }{ 5 } \)

Time taken to cover 90 km = 2hrs 30mins
= 150 minutes [\(\begin{matrix} 1hour=60minutes \\ 2hour=120mnutes \end{matrix}\)]
Time taken to cover 1 km = \(\frac { 150 }{ 90 } \) x 210 minutes
= 350 minutes
= 5 hours 50 minutes
Thus, the time taken to travel 210 km is 5 hours 50 minutes.

Using unitary method we can solve this as follows:
The cost of 2 notebooks = Rs. 24
The cost of 1 notebook = \(\frac { 24 }{ 2 } \) = Rs.12
Therefore, the cost of 9 notebooks = 9 x Rs.12
= Rs.108
Hence, Anbu has to pay Rs.108 for 9 notebooks.

Let x be the required number of charts.
As weight increases, the number of charts also increases. So the quantities are in direct proportion.
Hence \(\frac { { x }_{ 1 } }{ { y }_{ 1 } } =\frac { { x }_{ 2 } }{ { y }_{ 2 } } \)

\(\frac { 15 }{ 50 } =\frac { x }{ 2500 } \)
15 x 2500 = x \(\times\) 50
x \(\times\) 50 = 15 x 2500
x = \(\frac { 15\times 2500 }{ 50 } \) = 750
Therefore, 750 charts will weigh 2\(\frac {1}{2}\) kilogram.

Let x be the number of pencils required for 18 children. As the number of children increases, number of pencils also increases.
In the case of direct proportion we take \(\frac { { x }_{ 1 } }{ { y }_{ 1 } } =\frac { { x }_{ 2 } }{ { y }_{ 2 } } \)

\(\frac { 6 }{ 24 } =\frac { 18 }{ x } \)
\(\frac { 6\times x }{ 24 } \) = 18
x = \(\frac { 18\times 24 }{ 6 } \) = 72
Hence, 72 pencils are required for 18 children.