Answer: Option D. -> 50 days
Initially, Let there be x men having food for y days
After 10 days, x men had food for days (y - 10)
Also, $$\left( {x - \frac{x}{5}} \right)$$   men had food for y days
$$\eqalign{
& \therefore \,x\left( {y - 10} \right) = \frac{{4x}}{5} \times y \cr
& \Leftrightarrow 5xy - 50x = 4xy \cr
& \Leftrightarrow xy - 50x = 0 \cr
& \Leftrightarrow x\left( {y - 50} \right) = 0 \cr
& \Leftrightarrow y - 50 = 0 \cr
& \Leftrightarrow y = 50 \cr} $$

Answer: Option C. -> 3500
Let there be x men originally
So, x men had provisions 40 days whereas (x + 500) men consumed it in 35 days
More men, Less days (Indirect proportion)
$$\eqalign{
& \therefore \,\left( {x + 500} \right):x::40:35 \cr
& \Leftrightarrow 35 \times \left( {x + 500} \right) = 40x \cr
& \Leftrightarrow 5x = 35 \times 500 \cr
& \Leftrightarrow x = \left( {\frac{{35 \times 500}}{5}} \right) \cr
& \Leftrightarrow x = 3500 \cr} $$

Answer: Option C. -> Rs. 273
Cost of 21 pencils and 9 clippers = Rs. 819
Cost of 7 pencils and 3 clippers = $$\frac{{819}}{3}$$ = Rs. 273

Answer: Option B. -> 6
$$\eqalign{
& {\text{Work}}\,{\text{done}} = \frac{5}{8} \cr
& {\text{Balance}}\,{\text{work}} = {1 - \frac{5}{8}} = \frac{3}{8} \cr
& {\text{Let}}\,{\text{the}}\,{\text{required}}\,{\text{number}}\,{\text{of}}\,{\text{days}}\,{\text{be}}\,x \cr
& {\text{Then}}, \cr
&\frac{5}{8}:\frac{3}{8} :: 10:x \cr
& \Rightarrow \frac{5}{8} \times x = \frac{3}{8} \times 10 \cr
& \Rightarrow x = {\frac{3}{8} \times 10 \times \frac{8}{5}} \cr
& \Rightarrow x = 6 \cr} $$

Answer: Option B. -> 9
Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
$$\eqalign{
& \therefore 14:6::21:x \cr
& \Rightarrow 14 \times x = 6 \times 21 \cr
& \Rightarrow x = \frac{{6 \times 21}}{{14}} \cr
& \Rightarrow x = 9 \cr} $$

Answer: Option C. -> 7
Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
\[\left. \begin{gathered}
{\text{Spiders}}\,\,\,\,\,1:7 \hfill \\
\,\,\,{\text{Webs}}\,\,\,\,\,7:1 \hfill \\
\end{gathered} \right\}::7:x\]
$$\eqalign{
& \therefore 1 \times 7 \times x = 7 \times 1 \times 7 \cr
& \Rightarrow x = 7 \cr} $$

Answer: Option A. -> 48 paise
$$\eqalign{
& {\text{Let}}\,{\text{the}}\,{\text{required}}\,{\text{weight}}\,{\text{be}}\,x\,{\text{kg}}. \cr
& {\text{Less}}\,{\text{weight,}}\,{\text{less}}\,{\text{cost}}\,\left( {{\text{Direct}}\,{\text{Proportion}}} \right) \cr
& \therefore 250:200::60:x \cr
& \Rightarrow 250 \times x = {200 \times 60} \cr
& \Rightarrow x = \frac{{ {200 \times 60} }}{{250}} \cr
& \Rightarrow x = 48 \cr} $$

Answer: Option C. -> 40
Let the required number of days be x.
Less cows, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
\[\left. \begin{gathered}
{\text{Cows}}\,\,\,\,\,1:40 \hfill \\
{\text{Bags}}\,\,\,\,\,40:1 \hfill \\
\end{gathered} \right\}::40:x\]
$$\eqalign{
& \therefore 1 \times 40 \times x = 40 \times 1 \times 40 \cr
& \Rightarrow x = 40 \cr} $$

Answer: Option D. -> 12
Let the required number of working hours per day be x
More pumps, Less working hours per day (Indirect proportion)
Less days, More working hours per day (Indirect proportion)
\[\left. \begin{gathered}
{\text{Pumps 4}}:3 \hfill \\
\,\,\,\,\,\,{\text{Days 1}}:2 \hfill \\
\end{gathered} \right\}::8:x\]
$$\eqalign{
& \therefore {\text{ }}4 \times 1 \times x = 3 \times 2 \times 8 \cr
& \Leftrightarrow x = \frac{{\left( {3 \times 2 \times 8} \right)}}{{\left( 4 \right)}} \cr
& \Leftrightarrow x = 12 \cr} $$

Answer: Option D. -> Rs. 17100
Let the required earning be Rs. x
5 men = 7 women
7 men = $$ \left( \frac{7}{5} \times 7 \right) $$   women = $$\frac{49}{5}$$ women
∴ (7 men and 13 women)
$$\eqalign{
& = \left( {\frac{{49}}{5} + 13} \right){\text{women}} \cr
& = \frac{{114}}{5}{\text{ women}} \cr} $$
Now, More women, More earning (Direct proportion)
$$\eqalign{
& \therefore {\text{ }}7 : \frac{{114}}{5}::{\text{ 5}}250 : x \cr
& \Leftrightarrow 7x = \left( {\frac{{114}}{5} \times 5250} \right) \cr
& \Leftrightarrow 7x = 119700 \cr
& \Leftrightarrow x = 17100 \cr} $$