Comparing \(\frac { 1 }{ 4 } \)th of an inch and \(\frac { 3 }{ 8 } \)th of an inch.
\(\frac { 1 }{ 4 } =\frac { 2 }{ 8 } <\frac { 3 }{ 8 } \)
\(\therefore\) Second plant grew more.

Number of working days in an academic year = 220
\(\therefore\) Number of holidays = 365 - 220 = 145
\({Number \ of \ holidays\over Number \ of \ working \ days}={145\over220}={29\over44}\)
Number of holidays: No of working days = 29 : 44

5:4
\(\frac{5}{4}\times\frac{2}{2}=\frac{10}{8}=10:8\)
\(\frac{5}{4}\times\frac{3}{3}=\frac{15}{12}=15:12\)
Equivalent ratios of 5 : 4 are 10 : 8 and 15 : 12

75 : 100 
Fraction = \(\frac{75}{100} \div \frac{25}{25}=\frac{3}{4}\)
Simplest form = 3 : 4

12 : 27
Fraction = \(\frac{12}{27} \div \frac{3}{3}=\frac{4}{9}\)
Simplest form = 4 : 9

Matches won by Team A = 26 out of 52
\(\text { i.e: } \frac{26}{52}=1 / 2 \)
Matches won by team B = \(\frac { 3 }{ 4 } \times 52\) = 39 out of 52
∴ Team B won 39 out of 52 and therefore team B has the better record.

Number of times Antony brushes a day = 2
∴ Number of times Antony brushes a week = 2\(\times\)7 = 14
Number of times Shabeen brushes a day = 1
∴ Number of times Shabeen brushes a week = 1\(\times\)7 = 7
Number of times Antony brushes : Number of times Antony brushes =14 : 7 = 2 : 1
∴ The required ratio = 2 :1

1 hour = 60 minutes
Distance covered by cholan in 60 minutes = 6 km
Distance covered in one minutes = \(\frac{6}{60}\)
Distance covered in 20 minutes = \(\frac{6}{60} \times 20\)
= 2 km

Here the extremes are 3 and 20 and the means are 2 and 30.
Product of extremes, ad = 3 × 20 = 60.
Product of means, bc = 2 × 30 = 60.
Thus by proportionality law, we find ad = bc and hence 3 : 2 and 30 : 20 are in proportion.

Divide the whole money into 2 + 3 = 5 equal parts then, Vimala gets 2 parts out of 5 parts and Yazhini gets 3 parts out of 5 parts.
Amount Vimala gets =Rs. 600 ×\(2\over 5\) = Rs. 240
Amount Yazhini gets =Rs. 600 ×\(3\over 5\) =Rs. 360
Vimala received Rs. 240 and Yazhini gets Rs. 360, which is Rs. 120 more than that of Vimala.

In my purchase cost of 6 apples = Rs. 90
∴ cost of 1 apple = \(\frac { 90 }{ 6 } \) = Rs. 15
In my friend's purchase cost of 5 apples = Rs. 70
∴ Cost of apple =\(\frac { 70 }{ 5 } \) = Rs. 14
My friend buy for lower prize.
∴ My friend's purchase is a better buy.

(i) For Provisions:
Dividing the total amount Rs. 4000 into 3 + 2 = 5 equal parts then
3 out of 5 parts are spent for provisions & 2 out of 5 parts for vegetables
\(\therefore 4000\times\frac{3}{5}=2400\) for provisions
(ii) For vegetables:
\(4000\times\frac{2}{5}=1600\) for Vegetables
\(\therefore\) Rs.2400 spend on provisions & Rs.1600 spend on Vegetables