A man bought two types of sharpeners, one at ₹18 for 9 sharpeners and the other at ₹8 per sharpener. He purchased an equal number of each type and sold all the sharpeners at ₹8 per piece. Find his percentage profit.

Correct Answer: The correct option is 60%.

Step-by-step Explanation:

Step 1: Understand the cost price (CP) of both types of sharpeners.

Let us assume the man bought $x$ sharpeners of each type.

Type 1 Sharpeners:

Cost of 9 sharpeners = ₹18

Cost per sharpener of Type 1 = ₹18 / 9 = ₹2

Cost price of $x$ sharpeners of Type 1 = ₹2 × $x$ = ₹2$x$

Type 2 Sharpeners:

Cost per sharpener of Type 2 = ₹8

Cost price of $x$ sharpeners of Type 2 = ₹8 × $x$ = ₹8$x$

Step 2: Calculate the Total Cost Price (CP) for all sharpeners.

Total number of sharpeners bought = $x$ + $x$ = 2$x$

Total Cost Price (CP) = ₹2$x$ + ₹8$x$ = ₹10$x$

Step 3: Calculate the Total Selling Price (SP) for all sharpeners.

He sold all the sharpeners at ₹8 per piece.

Total Selling Price (SP) = 2$x$ × ₹8 = ₹16$x$

Step 4: Calculate total Profit and Percentage Profit.

Profit = Total SP - Total CP

Profit = ₹16$x$ - ₹10$x$ = ₹6$x$

Percentage Profit is given by the formula:

Profit Percentage = (Profit / Total CP) × 100

Profit Percentage = (6$x$ / 10$x$) × 100

Profit Percentage = (6 / 10) × 100 = 60%

Therefore, the man made a profit of 60%.