Solution:
$$\eqalign{ {\text{Let error}} = x{\text{ gms}}{\text{.}} \cr {\text{Then,}} \cr = \frac{x}{{1000 - x}} \times 100 = 25 \cr \Leftrightarrow \frac{{100x}}{{1000 - x}} = 25 \cr \Leftrightarrow 100x = 25000 - 25x \cr \Leftrightarrow 125x = 25000 \cr \Leftrightarrow x = 200 \cr \therefore {\text{Weight used}} \cr = (1000 - 200){\text{gms}} \cr = {\text{800 gms}}. \cr} $$

Solution:
In this type of question go through option
Option : C
Cost price = Rs. 50
Gains as much percentage as the cost price of the article means 50% gains
50% of cost price
50% of Rs. 50 = Rs. 25
Selling price = Cost price + Profit
Selling price = 50 + 25
Selling price = Rs. 75

Solution:

$${\text{Loss}} = \frac{4}{{80}} \times 100 = 10\% $$

$$\eqalign{ {\text{Profit}} = \frac{{200}}{{800}} \times 100 = 25\% \cr {\text{Over all profit}} \cr = 25 - 10 - \frac{{25 \times 10}}{{100}} \cr = 12.5\% {\text{ Answer}} \cr} $$

Solution:
$$33\frac{1}{3}\% = \frac{1}{3}$$
Let, selling price = 90
Let, SP = 3 × 3 = multiple of 9
SP₁ = $$\frac{1}{3}$$ × 90 = 30
(Cost price) = (Selling price) $$\left[ {\frac{{100}}{{100 - {\text{loss}}\% }}} \right]$$
= 30 × $$\frac{3}{2}$$
= 45
Original selling price 80% of
SP₂ = $$\frac{{80}}{{100}}$$ × 90 = 72
Profit = 72 - 45 = 27
Profit % = $$\frac{{27}}{{45}}$$ × 100 = 60%

Solution:
Given loss = 10% profit = 10%
Difference of overall profit and loss = 10 - (-10) = 20%
20% of cp = sp
$$\frac{{20}}{{100}} \times {\text{cp = 108}}$$
20 × cp = 108 × 100
cp = $$\frac{{10800}}{{20}}$$
∴ cp = 540

Solution:
Let the original price of the commodity be Rs. 100.
Increased price = Rs. 110
Price after discount
$$\eqalign{ = {\text{85}}\% {\text{ of Rs}}{\text{.110}} \cr {\text{ = Rs}}{\text{.}}\left( {\frac{{85}}{{100}} \times 110} \right) \cr = {\text{Rs}}{\text{. 93}}{\text{.50}}{\text{}} \cr} $$
∴ Discount on original price = (100 - 93.50)% = 6.5%

Solution:
Cost price of 28 articles = Selling price of 21 articles
$$\frac{{{\text{CP}}}}{{{\text{SP}}}} = \frac{{21}}{{28}} = \frac{3}{4}$$
Profit = Selling price - Cost price = 4 - 3 = 1
$$\eqalign{ {\text{Profit }}\% = \frac{1}{3} \times 100 \cr \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 33\frac{1}{3}\% \cr} $$