Solution:

Given data:
Mark up price = 20%
Discount given = 10%
Weight used = 900 grams
Actual weight = 1 kg

Let's consider the cost price of the dealer to be Rs. 100 for convenience.

Markup price:
The dealer marks up the price by 20%. Hence, the selling price becomes Rs. 120.

Discount given:
The dealer gives a discount of 10% on the selling price of Rs. 120. Hence, the customer pays Rs. 108.

Weight used:
The dealer uses a weight of 900 grams instead of 1 kg. Hence, the customer gets only 900/1000 of the product.

Actual selling price:
The actual selling price of the dealer becomes (108/0.9) * (1000/900) = Rs. 133.33 (approx).

Profit percentage:
Profit percentage = [(selling price - cost price)/cost price] * 100

Cost price = Rs. 100
Selling price = Rs. 133.33

Profit percentage = [(133.33 - 100)/100] * 100 = 33.33%

Hence, the dealer makes a profit of 33.33% due to these maneuvers.

Explanation:

The dealer uses two maneuvers to make a profit. Firstly, he marks up the price by 20%. This means that he increases the selling price by 20% from the cost price. Hence, he makes a profit of 20% on each product sold.

Secondly, he gives a discount of 10% to the customer. This means that he reduces the selling price by 10% from the marked up price. However, even after giving the discount, the selling price is higher than the actual selling price of the product. Hence, he still makes a profit of (selling price - cost price)/cost price * 100.

Lastly, he uses a weight of 900 grams instead of 1 kg. This means that the customer gets only 900/1000 of the product. Hence, the dealer makes a profit by selling less product for the same price.

Overall, the dealer makes a profit of 33.33% due to these maneuvers.

Say 1000 gm=1000 rps cp
marking up =20% so 1000+200=1200 mp
giving 10% discount =1200-120=1080 sp
and selling 900 gm instead of 1000 gm so

1000 gm=1000 rps
900 gm. =1080 rps

9*1000 gm=1000 rps*9=9000 cp
10*900 gm. =1080 rps*10=10800 sp
profit %
10800-9000/9000 =1800/9000=1/5=20% profit