Solution:
Total Mark obtain by all 50 student = 50 × 70 = 3500
Total mark obtain by 1st 25 student = 25 × 60 = 1500
Total mark obtain by next 24 student = 24 × 80 = 1920
Mark obtain by last student = 3500 - (1500 + 1920) = 80
i.e 80% mark obtain by last student.

Solution:
$$\eqalign{ 20\% \,{\text{of}}\,a = b \Rightarrow \frac{{20}}{{100}}a = b \cr \therefore b\% \,{\text{of}}\,20 = {\frac{b}{{100}} \times 20} \cr = {\frac{{20}}{{100}}a \times \frac{1}{{100}} \times 20} \cr = \frac{4}{{100}}a = 4\% \,\,{\text{of }}\,a \cr} $$

Solution:
Population after 2 years :
$$\eqalign{ = 8500 \times \left( {1 + \frac{{20}}{{100}}} \right)\left( {1 + \frac{{25}}{{100}}} \right) \cr = \left( {850 \times \frac{6}{5} \times \frac{5}{4}} \right) \cr = 12750 \cr} $$

Solution:
$$\eqalign{ 110 \times \frac{{\left( {100 - x} \right)}}{{100}} = 50 \times \frac{{\left( {100 + x} \right)}}{{100}} \cr 11\left( {100 - x} \right) = 5\left( {100 + x} \right) \cr 1100 - 11x = 500 + 5x \cr 16x = 600 \cr x = \frac{{800}}{{16}} = \frac{{75}}{2} = 37\frac{1}{2}\% \cr {\text{Now,}} \cr {\text{650}} \times \frac{{75}}{{200}} \to 780 \times \frac{{55}}{{200}} \cr \frac{{25}}{2} \to 11 \cr 25 \to 22 \cr = \frac{3}{{22}} \times 100 = 14\% \cr} $$

Solution:
Total sales tax paid = 7% of Rs. 400 + 9% of Rs. 6400
= Rs. $$\left( {\frac{7}{{100}} \times 400 + \frac{9}{{100}} \times 6400} \right)$$
= Rs. (28 + 576)
= Rs. 604
Total cost o the items :
= Rs. (400 + 6400)
= Rs. 6800
∴ Required percentage
$$\eqalign{ = \left( {\frac{{604}}{{6800}} \times 100} \right)\% \cr = 8\frac{{15}}{{17}}\% \cr} $$

Solution:
$$\eqalign{ 33\frac{1}{3}\% = \frac{1}{3} \cr {\text{Let income}} = 300 \cr {\text{Saving}} = 100 \cr {\text{Expenditure}} = 300 - 100 = 200 \cr} $$
\[\begin{array}{*{20}{c}} {}{{\text{Income}}} = {{\text{Expenditure}}} + {{\text{Saving}}} \\ {{\text{Old}} \to }{300} = {200} + {100} \\ {}{}{}{\,\,\,\,\,\,\,\,\,\,{ \downarrow ^{ + 10\% }}}{}{\,\,\,\,\,\,\,\,\,\,{ \downarrow ^{ + 22\% }}} \\ {{\text{New}} \to }x = {220} + {122} \end{array}\]
$$\eqalign{ x = 220 + 122 = 342 \cr {\text{Increase}} = 342 - 300 = 42 \cr {\text{Increase }}\% = \frac{{42}}{{300}} \times 100 = 14\% \cr} $$

Solution:
$$\eqalign{ {\text{Let}}\,{\text{the}}\,{\text{original}}\,{\text{price}} = y, \cr {\text{After}}\,{\text{first}}\,{\text{change,}}\,{\text{it}}\,{\text{becomes}}, \cr y \times \left( {1 + {\frac{x}{{100}}} } \right) \cr {\text{After}}\,{\text{second}}\,{\text{change,}}\,{\text{it}}\,{\text{becomes}} \cr y \times \left( {1 + {\frac{x}{{100}}} } \right)\left( {1 - {\frac{x}{{100}}} } \right) \cr = y\left( {1 - {{\left( {\frac{x}{{100}}} \right)}^2}} \right) \cr {\text{Thus}}, \cr {x^2} \times y = {10^6} - - - - \left( 1 \right) \cr {x^2} = \frac{{{{10}^6}}}{y} \cr {\text{Now}}, \cr y{\left( {1 - {\frac{{{{10}^6}}}{{10000y}}} } \right)^2} \cr = 2304\left( {{\text{similar}}\,{\text{to}}\,{\text{above}}} \right) \cr y{\left( {1 - \frac{{100}}{y}} \right)^2} = 2304 \cr y = 2500 \cr} $$