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.

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.

6 pumps filled the sump in hr 30 minutes = 90 minutes
Now, one pump in switched off.
Total no. of Pumps = 5

This is an inverse proportion, x₁y₁ = x₂y₂
6 x 90 = 5 \(\times\) x
\(x=\frac{6 \times 90}{5}\)
x = 108
The time taken to fill the pump = 108 minutes = 1 hr 48 minutes

30 men can reap a field in 15 days.
\(\therefore\) 1 men can reap the field in \(\cfrac { 15 }{ 30 } \) days = \(\cfrac { 1 }{ 2 } \)days
\(\therefore\) 20 men can reap the field in 10 days.

Since the given data are in direct proportion
\(\frac{x_{1}}{\mathrm{y}_{1}} =\frac{x_{2}}{\mathrm{y}_{2}} \)
\(\frac{1 / 2}{15} =\frac{8 \frac{1}{3}}{x} \)
\(\frac{1}{2} \times x =8 \frac{1}{3} \times 15 \)
\(\therefore x \Rightarrow \frac{25 \times 15 \times 2}{3}=250 \)
The cost of  \(8 \frac{1}{3}\) m cloth is Rs 250.

Let x be the required number of days. The decrease in number of workers lead to the increase in number of days. (Therefore, both are in inverse proportion)
For inverse proportion x₁y₁ = x₂ y₂

Hence 60 x 7 = 42 \(\times\) x
42 \(\times\) x = 60 x 7
x = \(\frac { 60\times 7 }{ 42 } \)
x = 10
In 10 days 42 workers can spin a bale of cotton.