For Rs 130 distance travelled = 100 km

300 can be travelled with Rs 390

In \(\cfrac { 1 }{ 2 } \) an hour number of words typed = 540
i.e., In 30 min No. of words typed = 540

= 18
In 12 minutes number of words typed = 18 X 12
= 216
216 words can be typed in 12 min

To produce 2.9 cm extension weight needed = 150 gm
To produce 1 cm extension weight needed = \(\cfrac { 150 }{ 2.9 } gm\)
\(\therefore\) To produce 17.4 cm extension weight needed  = \(\cfrac { 150\times 17.4 }{ 2.9 } gm\)
\(\therefore\) Weight of 900 gm will produce an extension of 17.4 cm

Six men can complete the work in 12 days.
After 2 days, the same six men can complete the remaining work in 10 days.
At the same time, 6 more men joined.
Total workers = 6 + 6 = 12 men
Let x be the number of days taken to complete the work.

This is inverse proportion
x₁y₁ = x₂y₂
6 x 10 = 12 x x
\(x=\frac{6 \times 10}{12}\)
x = 5
They will take 5 days to complete the remaining work.

Let x be the number of notebooks, bought for Rs. 1863

This is direct proportion
\(\frac{x_{1}}{y_{1}} =\frac{x_{2}}{y_{2}} \)
\(\frac{105}{2415} =\frac{x}{1863} \)
x x 2415 = 1863 x 105
\(x=\frac{105 \times 1863}{2415} \Rightarrow x=81\)
81 notebooks can be bought for Rs. 1863.

The cost of a dozen soaps = Rs. 396
ie., The cost of 12 soaps = Rs. 396
The cost of 1 soap = 33
The cost of 35 soaps = 33 x 35 = Rs. 1155

Let x be the amount of diesel to cover 1650 km.

This is a direct proportion.
\(\frac{x_{1}}{y_{1}} =\frac{x_{2}}{y_{2}} \)
\(\frac{108}{594} =\frac{x}{1650} \)
\(x =\frac{108 \times 1650}{594} \)
x = 300
300 litres diesel required to cover 1650 km.

6 cans of juice costs Rs. 210
1 can of juice costs \(=Rs. \frac{210}{6}=Rs. 35 \)
4 cans of juice costs = Rs. 35 x 4 = Rs. 140.

This is an inverse proportion,
\(x_{1} y_{1}=x_{2} y_{2}\)
30 x 10 = 25 x x
\(x=\frac{30 \times 10}{25}\)
x = 12 minutes
12minutes to take to print a book.

(i) Let x be the weight of the onions bought for Rs. 80.

This is a direct proportion,
\(\frac{x_{1}}{y_{1}}=\frac{x_{2}}{y_{2}} \)
\(\frac{7}{84}=\frac{x}{180} \)
84 x = 7 x 180
\(x=\frac{7 \times 180}{84} \Rightarrow x=15\)
Therefore 15 kg weight of the onions bought for Rs. 180.
(ii) 7 kg onions cost = Rs. 84
1 kg onions cost = Rs. 12
3 kg onions cost = 3 x 12 = Rs. 36

To cover 100 km quantity of petrol required = 2 litres
\(\therefore\) To cover 1km petrol required = 2litres
To cover 1km petrol required = \(\cfrac { 2 }{ 100 } =\cfrac { 1 }{ 50 } litres\)
\(\therefore\) To cover 250km petrol required = \(\cfrac { 1 }{ 50 } \times 250=5litres\)
5 litres of petrol required to cover 250 km

Valli purchases 10 pens for Rs. 180
\(\therefore\) Valli purchase 1 pen for \(Rs.\frac {180}{10} =Rs.18\)
Kamala buys 8 pens for Rs. 96
\(\therefore\) Kamala buys 1 pen for \(Rs. \frac {96}{8} =Rs.12\)
= Rs. 12
\(\therefore\) Kamala bought the pen cheaper.

The weight of 72 books = 9 kg
The weight of 1 book = \(\frac{9}{72} \mathrm{~kg}\)
The weight of 40 books \(=\frac{9}{72} \times 40=5 \mathrm{~kg}\)

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.

Since the given data are in direct proportion
\(\frac{x_{1}}{y_{1}}=\frac{x_{2}}{y_{2}}\)
\(\frac{8}{120}=\frac{12}{x}\)
8x = 120 x 12
\(\therefore x=\frac{120 \times 12}{8}=180\)
In 12 trips, 180 people would have attended the party.