1. Profit and Loss

Medium Acceptance: 58.4%

A shopkeeper sells an article at a loss of 12.5%. Had he sold it for Rs. 51.80 more, he would have gained 6%. Find the cost price (CP) of the article.

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Profit and Loss Quantitative Aptitude

Medium

A shopkeeper sells an article at a loss of 12.5%. Had he sold it for Rs. 51.80 more, he would have gained 6%. Find the cost price (CP) of the article.

Interactive Visual Explanation

Step 1 of 3

Step 1

Understand the Percentage Points

The problem describes two scenario outcomes: a Loss of 12.5% and a Gain of 6%. Cost Price (CP) represents the 100% baseline.

\text{Baseline CP} = 100\%

Step 2

Represent the Difference mathematically

A loss of 12.5% means the selling price is 87.5% of CP. A gain of 6% means the selling price is 106% of CP. The difference between these two points is given as Rs. 51.80.

Visual Concept Model Hover elements to inspect values

Loss Side: 87.5% CP + Gain Side: 106% CP = 18.5% of CP (Rs. 51.80)

106\% - 87.5\% = 18.5\% \text{ of CP}

Step 3

Solve for the Cost Price (100%)

Since 18.5% of the Cost Price is Rs. 51.80, we can calculate the total 100% Cost Price using basic division:

\text{CP} = \frac{51.80 \times 100}{18.5} = \text{Rs. } 280

⚡

CGL Exam Speed Trick

⚡ CGL Speed Trick: Don't draw equations! Simply add the loss and gain percentages when they are on opposite sides of CP: $12.5\% + 6\% = 18.5\%$. Now divide the price change by this percentage: $51.80 / 18.5 = 2.8$. Multiply by 100 to get the answer: 280. You can do this in 8 seconds!

⚡ Speed-Run CGL Cheatsheet

Mastering these core principles will let you solve similar questions under 30 seconds.

Core Identity:

Price Difference / Percentage Difference = Cost Price

Check the interactive visualizer in the first tab to see these formulas modeled geometrically!

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