Solution:
$$\eqalign{ {\text{C}}{\text{.P}}{\text{. = Rs}}{\text{. 4900}}{\text{.}} \cr {\text{S}}{\text{.P}}{\text{. = 110}}\% {\text{ of Rs}}{\text{.4900}} \cr {\text{ = Rs}}{\text{.}}\left( {\frac{{110}}{{100}} \times 4900} \right) \cr = {\text{Rs}}{\text{. 5390}}{\text{.}} \cr {\text{Let marked price be Rs}}{\text{.}}x \cr {\text{Then,}} \cr {\text{ = 87}}\frac{1}{2}\% {\text{ of }}x{\text{ = 5390}} \cr \Rightarrow \left( {\frac{{175}}{2} \times \frac{1}{{100}} \times x} \right) = 5390 \cr \Rightarrow x = \left( {\frac{{5390 \times 8}}{7}} \right) = 6160 \cr \therefore {\text{Marked price}} = {\text{Rs}}{\text{.6160}} \cr} $$

Solution:
We find the net profit in each case :
1 → In this case, profit = 10%
$$\eqalign{ 2 \to {\text{Profit}} = \left( {\frac{{100}}{{900}} \times 100} \right)\% \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 11\frac{1}{9}\% \cr} $$
3 → Let C.P. of sugar be Rs. 1 per kg

Then, he mixes 100 gm impurities and realizes the C.P. of 1.1 kg sugar by selling 1 kg of sugar.
S.P. of sugar = Rs. 1.10 per kg.
$$\eqalign{ \therefore {\text{Profit}} = \left( {\frac{{0.1}}{1} \times 100} \right)\% \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$
4 → Let C.P. of sugar be Rs. 1 per kg.
Since he weighs 950 gm instead of a kg, his actual
C.P. = Rs. 0.95
S.P. = 105% of Rs. 1 = Rs. 1.05
$$\eqalign{ \therefore {\text{Profit}} = \left( {\frac{{0.10}}{{0.95}} \times 100} \right)\% \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\frac{{10}}{{19}}\% \cr} $$
Clearly, the maximum profit is earned when he used a 900 gm weight for a kg.

Solution:
Let cost price of hand cart = 100
According to the question,
\[{\text{100 (cp)}}\xrightarrow{{25\% {\text{Loss}}}}75{\text{ }}({\text{sp}})\xrightarrow{{ \times \frac{{48}}{5}}}720\,{\text{(given)}}\]
$$\eqalign{ 75\,{\text{units}} \to 720 \cr 1\,{\text{unit}} \to \frac{{720}}{{75}} = \frac{{48}}{5} \cr 100\,{\text{units}} \to \frac{{48}}{5} \times 100 = 960 \cr \therefore {\text{Cost price}} = {\text{ Rs}}{\text{.960}} \cr {\text{To gain }}25\% {\text{ selling price is }} \cr = {\text{cp}} + {\text{profit}}\% \times {\text{cp}} \cr = 960 + \frac{{25}}{{100}} \times 960 \cr = 960 + 240 = {\text{Rs}}{\text{.}}\,1200 \cr} $$

Solution:
$$\eqalign{ {\text{MP}} = M \cr {\text{SP}} = \frac{M}{2} \cr \% \,{\text{Discount}} \cr = {\frac{{ {\frac{M}{2}} }}{M}} \times 100 \cr = 50\% \cr} $$

Solution:
Let the labelled price be Rs. x.
Then,
(80% of x) - (75% of x) = 500
⇒ 5% of x = 500
$$\eqalign{ \Rightarrow x = \left( {\frac{{500 \times 100}}{5}} \right) \cr \,\,\,\,\,\,\,\,\,\,\,\,\, = 10000 \cr = {\text{Rs}}{\text{. }}10,000 \cr} $$
∴ Purchase is = 10000 - 20% of 10000
= Rs.8000

Solution:
Cost price of 10 toffees = Rs. 15
Cost price of 80 toffees = Rs. 120
Selling price of 16 toffees = Rs. 40
Selling price of 80 toffees = Rs. 200
∴ Profit = 200 - 120 = Rs. 80
∴ Profit % = $$\frac{{80}}{{120}}$$ × 100 = 66.67%

Solution:
$$\eqalign{ {\text{Let C}}{\text{.P}}{\text{. be Rs}}{\text{. }}x \cr {\text{Then,}} \cr 107\frac{1}{2}\% {\text{ of }}x - 92\frac{1}{2}\% {\text{ of }}x = 3 \cr \Rightarrow \frac{{215}}{{200}}x - \frac{{185}}{{200}}x = 3 \cr \Rightarrow \frac{{30x}}{{200}} = 3 \cr \Rightarrow x = 20 \cr} $$