By selling 8 dozen pencils, a shopkeeper gains an amount equal to the selling price of 1 dozen pencils. Determine the gain percentage.

Introduction:Profit statements expressed as a multiple of selling price are common. Converting these descriptions to algebra with per-dozen or per-unit prices helps to compute the gain percentage accurately.

Given Data / Assumptions:

• Let S be the selling price per dozen pencils.
• By selling 8 dozen, the profit equals S (the price of 1 dozen).
• All dozens are sold at the same price.

Concept / Approach:Total SP for 8 dozen is 8S. If profit equals S, then total cost for 8 dozen must be 8S - S = 7S. Profit percentage is profit divided by cost times 100.

Step-by-Step Solution:Total SP for 8 dozen = 8SProfit = STotal CP = 8S - S = 7SProfit% = S / 7S * 100 = 100/7% = 14 2/7%

Verification / Alternative check:Use numbers: suppose S = Rs 700 per dozen. Then 8S = Rs 5600; profit S = Rs 700; cost = Rs 4900. Profit% = 700/4900 * 100 = 14.2857...% = 14 2/7%.

Why Other Options Are Wrong:

• 12.5%: too small; comes from mixing dozen and unit counts.
• 20%: too large; results from taking S over 5S or similar mistakes.
• None of these: incorrect because 14 2/7% is exact.

Common Pitfalls:

• Treating S as CP rather than SP.
• Forgetting that percentage is on cost, not selling price.

Final Answer:14 2/7%