Solution:

If the seller is buying at Rs.12/liter and mixing it with 20% of water and selling it for Rs.15/liter, he is selling the thus formed 1.2 liters of mixture at Rs.18

Thus the percentage of his gain is 50%.

Solution:

Let us assume that the purchase price is Rs. 100, then the selling price at the loss of 12 1/2 % will be Rs. 87.5.

Thus the ratio of purchasing price and selling price when the loss is 12 1/2 %
= 100/87.5 = 8/7 or 8:7.

Solution:

Let us assume that he bought 100 Kg of antique stones for Rs. 100.

Then he sold the same stones for Rs. 90 while making a profit of 15%.

Thus CP of the sold stones = 90/1.15 = Rs. 78.26

Thus it means that the merchant sold 78.26 Kg in place of 100 Kg

Or we can frame the sentence as he is weighing 78.26 Kg for 100 Kg.

Solution:

Let the cost prices of the cell phones be x and 8000 - x

Now the selling price of both of the phones is same
Thus
(140/100)*x = (60/100)*(8000-x)
x = 2400

Thus one of the cell phone has a cost price of 2400 whereas the other phone has the cost price of (8000 - 2400) or 5600.

Solution:

Suppose that the market price was Rs.100.

Now when the successive discounts were applied, the selling price will become 80 and 75 respectively with each discount.

Thus the selling price has become rs.75 but he managed a profit of 20%

Thus
Cost price = (75/120)*100 = 62.5

Percent Increase with respect to the market price = (37.5/62.5)*100
= 60%

Solution:

Let us assume I bought 100 m of cloth for 100 Rs.
Thus I must be selling the cloth for Rs. 90 (10 percent loss).

But using false measurement, I gained a profit of 15 percent

Thus CP of the sold cloth = 90/1.15 = Rs. 78.26

Thus I must have sold 78.26 meters in place of 100 meters.