Solution:
$$\eqalign{ {\text{Let the rate of be R}}\% {\text{p}}{\text{.a}}{\text{.}} \cr Then, \cr {\frac{{600 \times R \times 4}}{{100}}} + {\frac{{600 \times R \times 2}}{{100}}} = 180 \cr \Rightarrow 2400{\text{R}} + 1200{\text{R}} = 18000 \cr \Rightarrow 3600{\text{R}} = 18000 \cr \Rightarrow {\text{R}} = 5\% \cr} $$

Solution:
$$\eqalign{ {\text{Principal}} \cr = Rs.\,\left( {\frac{{100 \times 4016.25}}{{9 \times 5}}} \right) \cr = Rs.\,\left( {\frac{{401625}}{{45}}} \right) \cr = Rs.\,8925 \cr} $$

Solution:
Capital after paying income tax
$$\eqalign{ \Rightarrow {\text{4}}\% - {\text{3}}{\text{.75}}\% = {\text{48}} \cr \Rightarrow {\text{0}}{\text{.25}}\% {\text{ = 48}} \cr {\text{100}}\% {\text{ = }}\frac{{48}}{{0.25}} \times 100 \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19200 \cr} $$
⇒ Capital without paying income tax
⇒ 19200 = Capital × 96%
Net capital = 20000

Solution:
$$\eqalign{ {\text{Let rate is }}R\% \cr {\text{We have}}, \cr I = \frac{{PTR}}{{100}} \cr {\text{Here}},1500 = \frac{{5000 \times 3 \times R}}{{100}} \cr {\text{Thus}},R = 10\% \cr} $$

Solution:
$$\eqalign{ {\text{Rate of interest}} = {\text{5}}\% {\text{ p}}{\text{.a}}{\text{.}} \cr {\text{sum}} = {\text{Rs}}{\text{. 3200}} \cr {\text{Time}} = {\text{2 years 6 months}} \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\frac{1}{2}{\text{years}} \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{5}{2}{\text{years}} \cr {\text{S}}{\text{.I}}{\text{.}} = \frac{{{\text{Prinicipal}} \times {\text{Time}} \times {\text{Rate}}}}{{100}} \cr \,\,\,\,\,\,\,\,\,\, = \frac{{3200 \times 5 \times 5}}{{2 \times 100}} \cr \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}400 \cr \therefore {\text{Amount}} = {\text{Rs}}{\text{. sum}} + {\text{S}}{\text{.I}}. \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {3200 + 400} \right) \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. 3600}}{\text{}} \cr} $$

Solution:
$$\eqalign{ {\text{Interest}}\,{\text{for}}\,{\text{the}}\,{\text{last}}\,{\text{5}}\,{\text{years}} \cr = \frac{{PTR}}{{100}} \cr = \frac{{360 \times 5 \times 6}}{{100}} = Rs.\,108 \cr {\text{Interest}}\,{\text{for}}\,{\text{year}} = 540 - 360 = 180 \cr {\text{So,}}\,{\text{interest}}\,{\text{for}}\,{\text{first}}\,{\text{four}}\,{\text{years}} \cr = 180 - 108 = Rs.\,72; \cr {\text{Now,}}\,{\text{rate}}\,{\text{for}}\,{\text{first}}\,{\text{four}}\,{\text{years}} \cr = \frac{{ {72 \times 100} }}{{360 \times 4}} \cr = 5\% \cr} $$

Solution:
$$\eqalign{ \frac{{P \times 5.4 \times 9.25}}{{100}} = \left( {14395.20 - P} \right) \cr P = 9600 \cr \frac{{9600 \times 8.6 \times 4.5}}{{100}} = {\text{SI}} \cr {\text{SI}} = 3715.20 \cr} $$