Maximum possible number of tables = 6

[ &\#8757; 1200 $\times$ 6 = 7200]

Number of chairs purchased \begin{align} & {\text{ = }}\frac{{{\text{8100}} - {\text{7200}}}}{{{\text{300}}}}{\text{ = }}\frac{{{\text{900}}}}{{{\text{300}}}}{\text{ = 3}}{\text{.}} \cr & {\text{Hence, }} \cr & {\text{Required ratio}} = {\text{3}}:{\text{6}} \cr & {\text{ = 1}}:{\text{2}} \cr\end{align}

Cu : Zn =5 : 2 = 5x :2x

5x+2x= 17.5 kg

7x =17.5

x = 2.5 Kg

cu =2.5*5=12.5 kg

zn= 2x=2*2.5=5 kg

adding 1.25 kg zn will cause

Cu: Zn= 12.5:(5+1.25)= 12.5:6.25=2:1

Let the incomes of A, B, C be 7x, 9x and 12x and their expenditures be 8y, 9y and 15y respectively

Then, A's saving = (7x - 8y) \begin{align} & \therefore 7x - 8y = \frac{1}{4}{\text{of }}7x \cr & \Rightarrow 8y = 7x - \frac{{7x}}{4} \cr & \Rightarrow 8y = \frac{{21}}{4}x \cr & \Rightarrow y = \frac{{21}}{{32}}x. \cr & {\text{So, A's expenditure}} \cr & = \left( {8 \times \frac{{21}}{{32}}x} \right) = \frac{{168}}{{32}}x; \cr & {\text{B's expenditure}} \cr & = \left( {9 \times \frac{{21}}{{32}}x} \right) = \frac{{189}}{{32}}x; \cr & {\text{C's expenditure}} \cr & = \left( {15 \times \frac{{21}}{{32}}x} \right) = \frac{{315}}{{32}}x; \cr & \therefore {\text{A's saving}} \cr & = \left( {7x - \frac{{168}}{{32}}x} \right) = \frac{{56}}{{32}}x; \cr & \therefore {\text{B's saving}} \cr & = \left( {9x - \frac{{189}}{{32}}x} \right) = \frac{{99}}{{32}}x; \cr & \therefore {\text{C's saving}} \cr & = \left( {12x - \frac{{315}}{{32}}x} \right) = \frac{{69}}{{32}}x; \cr & {\text{Hence, required ratio}} \cr & = \frac{{56}}{{32}}x:\frac{{99}}{{32}}x:\frac{{69}}{{32}}x \cr & = 56:99:69. \cr\end{align}

Let the terms of the ratio be x and x + 40. \begin{align} & {\text{Then, }} \cr & = \frac{x}{{x + 40}} = \frac{2}{7} \cr & \Rightarrow 7x = 2x + 80 \cr & \Rightarrow 5x = 80 \cr & \Rightarrow x = 16. \cr & \therefore {\text{Required ratio}} \cr & = 16:56 \cr\end{align}

Let the fourth proportional to 0.12, 0.21 and 8 be x. \begin{align} & {\text{Then, }} \cr & = {\text{0}}{\text{.12}}:{\text{0}}{\text{.21}}::{\text{8}}:x \cr & \Rightarrow {\text{0}}{\text{.12}}x = 0.21 \times 8 \cr & \Rightarrow x = \frac{{0.21 \times 8}}{{0.12}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, = \frac{{21 \times 8}}{{12}} \cr & \, \, \, \, \, \, \, \, \, \, \, \, = 14. \cr\end{align}