Solution:
Total Amount = Rs. 56
Number of coins Ratio of 50 paise coin and 25 paise coins = 2 : 1
Number of coins Ratio of Rs. 1 coin and 50 paise coins = 1 : 4
∴ Number of coins Ratio of Rs. 1 : 50 paise : 25 paise = 1 : 4 : 2

Ratio of coin's value
Rs. 1 : 50 paise : 25 paise (value) = 1 : 2 : 0.50
(Multiply by 2 to remove the fraction value in above ratio)
i.e Rs. 1 : 50 paise : 25 paise (value) = 2 : 4 : 1
Value of 50 paise coin in Rs. 56 = $$\frac{4}{{7}} \times 56 = 32 $$
Number of 50 paise coin is = 32 × 2 = 64

Solution:
1 day = 24 hours.
∴ Given ration = 3 : 24
= 1 : 8

Solution:
Given;
7 jumps of Tom = 5 jumps of Jerry
Or, $$\frac{{{\text{Tom}}}}{{{\text{Jerry}}}} = \frac{5}{7}$$
Let Jerry's 1 leap = 7 meter and Tom's 1 leap = 5 meter
Then, ratio of speed of Tom and Jerry
= $$\frac{{8 \times 5}}{{6 \times 7}}$$
= $$\frac{{40}}{{42}}$$
= 20 : 21

Solution:
Let A = 2k, B = 3k, C = 5k
A = x% of (B + C)
⇒ 2k = x% of (3k + 5k) = x% of 8k
$$\eqalign{ \Rightarrow \frac{x}{{100}} = \frac{{{\text{2k}}}}{{{\text{8k}}}} = \frac{1}{4} \cr \Rightarrow x = \frac{{100}}{4} = 25 \cr} $$

Solution:
$$\eqalign{ a:b = b:c \cr \frac{a}{b} = \frac{b}{c} \cr {b^2} = ac \cr {b^4} = {a^2}{c^2} \cr \therefore {a^4}:{b^4} = \frac{{{a^4}}}{{{b^4}}} \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^4}}}{{{a^2}{c^2}}} \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^2}}}{{{c^2}}} \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {a^2}:{c^2} \cr} $$

Solution:
$$\eqalign{ 20\% \,{\text{of A}} = 30\% \,{\text{of B}} = \frac{1}{6}{\text{of C}} \cr \Rightarrow \frac{{20{\text{A}}}}{{100}} = \frac{{30{\text{B}}}}{{100}} = \frac{{\text{C}}}{{\text{6}}} \cr \Rightarrow \frac{{\text{A}}}{5} = \frac{{3{\text{B}}}}{{10}} = \frac{C}{6} = k(say) \cr \Rightarrow A = 5K,\,B = \frac{{10k}}{3},\,C = 6k \cr \therefore {\text{A}}:{\text{B}}:{\text{C}} = 5k:\frac{{10k}}{3}:6k \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5:\frac{{10}}{3}:6 \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 15:10:18 \cr} $$

Solution:
$$\eqalign{ {\text{A}}:{\text{B}} = 5:12 \cr {\text{B}}:{\text{C}} = 4:5.50 \cr \,\,\,\,\,\,\,\,\,\,\,\,\, = 12:16.5 \cr \,\,\,\,\,\,\,\,\,\,\,\,\, = 12:\frac{{33}}{2} \cr {\text{A}}:{\text{B}}:{\text{C}} = 5:12:\frac{{33}}{2} \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10:24:33 \cr {\text{Sum of ratio terms}} \cr = 10 + 24 + 33 \cr = 67 \cr {\text{C's share}} = {\text{Rs}}{\text{.}}\left( {2010 \times \frac{{33}}{{67}}} \right) \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}990 \cr B'{\text{s share}} = {\text{Rs}}{\text{.}}\left( {2010 \times \frac{{24}}{{67}}} \right) \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.720 \cr {\text{Required difference}} \cr = {\text{Rs}}{\text{.}}\left( {990 - 720} \right) \cr = {\text{Rs}}{\text{. }}270 \cr} $$