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A man bought pencils at the rate of 6 fo...

A man bought pencils at the rate of 6 for Rs. 4 and sold them at the rate of 4 for Rs. 6. His gain in the transaction is:

A

`75%`

B

`80%`

C

`125%`

D

`100%`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will first determine the cost price (CP) and selling price (SP) of the pencils, and then calculate the gain. ### Step 1: Determine the Cost Price (CP) The man bought pencils at the rate of 6 for Rs. 4. To find the cost price of one pencil: - Cost of 6 pencils = Rs. 4 - Cost of 1 pencil = Rs. 4 / 6 = Rs. 2/3 ### Step 2: Determine the Selling Price (SP) The man sold pencils at the rate of 4 for Rs. 6. To find the selling price of one pencil: - Selling price of 4 pencils = Rs. 6 - Selling price of 1 pencil = Rs. 6 / 4 = Rs. 3/2 ### Step 3: Calculate the Cost Price for 12 Pencils To make calculations easier, we will consider 12 pencils (the least common multiple of 6 and 4). - Cost of 12 pencils = 12 * (Rs. 2/3) = Rs. 8 ### Step 4: Calculate the Selling Price for 12 Pencils Now, we will calculate the selling price for 12 pencils. - Selling price of 12 pencils = 12 * (Rs. 3/2) = Rs. 18 ### Step 5: Calculate the Gain Gain = Selling Price - Cost Price - Gain = Rs. 18 - Rs. 8 = Rs. 10 ### Step 6: Calculate the Gain Percentage Gain Percentage = (Gain / Cost Price) * 100 - Gain Percentage = (Rs. 10 / Rs. 8) * 100 = 125% Thus, the man's gain in the transaction is **125%**. ---
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