\(\frac { 40 }{ 5 } =\frac { 8 }{ 1 } \)
\(\frac { 42 }{ 6 } =\frac { 7 }{ 1 } \)
\(\because\) 8 > 7
\(\therefore\) First shopkeeper is costlier
\(\therefore\) Tomatoes must be purchased from the second shopkeeper.
The comparison by taking difference will not help him decide as the weights of tomatoes  purchased from the two shopkeepers are different.
 

Ratio of sides of triangle = 2 : 3 : 5
Total perimeter = 70
Total of the ratio of sides = 2 + 3 + 5 =10
\(\therefore\) Length of the longest side = \(70\times\frac{5}{10}=35\ cm\)

Runs made by Anish in 6 overs = 42
\(\therefore\) Runs made by Anish in 1 over \(=\frac{42}{6}=7\)
Runs made by Anup in 7 overs = 63
\(\therefore\) runs made by Anup in 1 over \(=\frac{63}{7}=9\)
\(\because\) 9>7
Hence, Anup made more runs per over.

For Raju, cost of 10 pens = Rs.150
\(\therefore\) Cost of 1 pen \(=Rs.\frac{150}{10}=Rs.15\)
For Manish, cost of 7 pens = Rs.84
\(\therefore\) Cost of 1 pen \(=Rs.\frac{84}{7}=Rs.12\)
Here, Rs.12 < Rs.15
Hence, Manish got the pens cheaper.

Given, weight of 72 books = 9 kg
\(\therefore\) Weight of 1 book \(=\frac{9}{72}\ kg\)
\(\therefore\) Weight of 40 books \(=\frac{9}{72}\times40\ kg=\frac{360}{72}\ kg=\frac{360\div72}{72\div72}=5\ kg\)
[\(\because\)HCF of 360 and 72 = 2 X 2 X 2 X 3 X 3 = 72]
Hence, the weight of 40 books is 5 kg.

Given, in last 30 days, temperature drop = 15 degree
\(\therefore\) In 1 day, temperature drop \(=\frac{15}{30}\) degree
\(=\frac{15\div15}{30\div15}=\frac{1}{2}degree[\because \ HCF\ of\ 15\ and\ 30=15]\)
\(\therefore\) In next 10 days, temperature drop
\(=\frac{1}{2}\times10\ degree=5\ degree\)
Hence, temperature dropped 5 degree in the next 10 days.

Here,the number of days is known and rain fall is unknown. Given, rainfall in 3 days = 276 mm
\(\therefore\) Rainfall in 1 day \(=\frac{276}{3}=92 mm\)
\(\therefore\) Rainfall in one full week i.e. 7 days = 92 X 7 = 644 mm In centirnerre, rainfall in one full week
\(=644\times\frac{1}{10}\ cm=64.4\ cm [\because 1\ mm=\frac{1}{10}\ cm]\)
Hence,644 mm or 64.4 cm rain will fall in 7 days or one fullweek.

8:9

We have,Rs.10:Rs.15=10:15 and 4:6
Now, 10:15=\(\frac{10}{15}=\frac{10\div5}{15\div5}\)
\(\because\) 10= 2 X 5 and 15 = 3 X 5
\(\therefore\) HCF of 10 and 15
\(\frac{2}{3}=2:3\ and\ 4:6=\frac{4}{6}=\frac{4\div2}{6\div2}=\frac{2}{3}=2:3\)
[dividing numeraror and denominaror by 2]
Here, 10 : 15 = 4 : 6 = 2 : 3 i.e. 10 : 15 and 4 : 6 are in proportion.
Thus, the proper form is 10 : 15 : : 4 : 6.

We have, 4: 12 and 9: 27
Here, \(4:12=\frac{4}{12}=\frac{4\div4}{12\div4}=\frac{1}{3}=1:3\)
[dividing numerator and denominator both by 4]
Now, \(9:27=\frac{9}{27}=\frac{9\div9}{27\div9}=\frac{1}{3}-1:3\)
[dividing numerator and denominator both by 9]
Hence, 4 : 12=9: 27=1: 3 i.e.4: 12 and 9:27are in proportion.
Thus, the proper form is 4: 12: : 9 : 27.

We have, 15 : 45 and 5 : 25
Here, \(15:45=\frac{15}{45}=\frac{15\div15}{45\div15}\)
[dividing numerator and denominator both by 15]
\(=\frac{1}{3}=1:3\ and\ 5:25=\frac{5}{25}=\frac{5\div5}{25\div5}=\frac{1}{5}=1:5\)
[dividing numerator and denominator both by 5]
Here, 15 : 45 \(\ne\)5 : 25
Thus, 15 : 45 and 5 : 25 are not in proportion.

No

8:11

3:4

Given, cost of 12 pens = Rs.180
\(\therefore\ Cost\ of\ 1\ pen=\frac{Total\ cost\ of\ pens}{Number\ of\ pens}=Rs.\frac{180}{12}=Rs.15\) [\(\because\)1 dozen = 12 units]
Also given, cost of 8 ball pens = Rs.56
\(\therefore\ Cost\ of\ 1\ ball\ pen=\frac{Total\ cost\ of\ ball\ pens}{Number\ of\ ball\ pens}=\frac{Rs.15}{Rs.7}=\frac{15}{7}=15:7\)