Gita sells two objects A and B at the same price such that she makes a profit of **20%** on object A and a loss of **10%** on object B. If she increases the selling price such that objects A and B are still sold at an equal price and a profit of **10%** is made on object B, then the profit made on object A will be nearest to:

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Let the cost price of object A be $$ A $$ and the cost price of object B be $$ B $$.

#### Step 1: Initial selling prices
- Gita makes a profit of **20%** on object A, so the selling price of A is:  
$$ 	ext{Selling Price of A} = 1.2A. $$  
- Gita incurs a loss of **10%** on object B, so the selling price of B is:  
$$ 	ext{Selling Price of B} = 0.9B. $$

Since both objects are sold at the same price:  
$$ 1.2A = 0.9B \quad 	ext{or} \quad B = \frac{4}{3}A. $$

#### Step 2: New selling prices
Gita increases the selling price such that a profit of **10%** is made on object B. The new selling price of B is:  
$$ 	ext{New Selling Price of B} = 1.1B. $$

Substitute $$ B = \frac{4}{3}A $$ into the equation:  
$$ 	ext{New Selling Price of B} = 1.1 	imes \frac{4}{3}A = \frac{44}{30}A = 1.466A. $$

Since both objects are sold at the same price, the new selling price of A is also $$ 1.466A $$.

#### Step 3: Profit percentage on object A
The profit percentage on object A is calculated as:  
$$ 	ext{Profit Percentage on A} = \frac{	ext{Selling Price - Cost Price}}{	ext{Cost Price}} 	imes 100. $$

Substitute values:  
$$ 	ext{Profit Percentage on A} = \frac{1.466A - A}{A} 	imes 100 = (0.466) 	imes 100 = 46.6\%. $$

Thus, the profit made on object A is approximately **47%**.

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