Question

A dishonest shopkeeper uses faulty weights while selling goods. He uses a fake 1kg weight that weighs 800gms and marks the price up by 20%. If 25% of the goods he received were defective, by how many percentage points should he increase the markup percentage so that the profit percentage remains unaffected?

• A. 20
• B. 40
• C. 10
• D. 75
• E. 25

Hint:

For complex profit problems, it's often easiest to assume a base Cost Price (like \$100) and work through each condition step-by-step. First, find the baseline profit percentage. Then, adjust the cost and revenue calculations based on the new conditions to find the variable required to meet the baseline profit.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This is a multi-step profit and loss problem involving faulty weights, markups, and defective goods. We first need to calculate the original profit percentage and then find the new markup required to maintain it under new conditions.
Step 2: Detailed Explanation:
Let's assume the Cost Price (CP) of 1000 gm of goods is \$100.
Part 1: Calculate the original profit percentage.

Markup: The shopkeeper marks the price up by 20%. \[ \text{Marked Price (MP) of 1000 gm} = \$100 \times (1 + 0.20) = \$120 \]
Faulty Weight: He uses an 800 gm weight to sell 1 kg. So, when a customer buys "1 kg", they are actually getting 800 gm.
Revenue: The selling price (SP) for 800 gm is the MP of 1000 gm, which is \$120.
Cost: The cost of the 800 gm he sells is \( \frac{800}{1000} \times \$100 = \$80 \).
Profit: Profit = SP - CP = \$120 - \$80 = \$40.
Profit Percentage: \[ \text{Profit %} = \left(\frac{\text{Profit}}{\text{CP}}\right) \times 100 = \left(\frac{\$40}{\$80}\right) \times 100 = 50% \]
So, the original profit percentage is 50%.
Part 2: Calculate the new markup with defective goods.

Defective Goods: 25% of the goods are defective. This means for every 1000 gm he buys for \$100, only 750 gm are sellable.
Effective Cost: His effective cost for 750 gm of sellable goods is \$100.
Goal: He wants to maintain a 50% profit on this effective cost. \[ \text{Target Profit} = 50% \text{ of } \$100 = \$50 \] \[ \text{Target Revenue} = \text{Effective Cost} + \text{Target Profit} = \$100 + \$50 = \$150 \]
He must generate \$150 in revenue by selling the 750 gm of good stock, using his 800 gm fake weight. Let the new markup be \(m%\).
New Marked Price (MP') of 1000 gm = \( \$100 \times (1 + \frac{m}{100}) \).
The revenue from selling 800 gm is MP'. So the revenue from 1 gm is \( \frac{\text{MP'}}{800} \).
The total revenue he can get from his 750 gm of goods is: \[ \text{Total Revenue} = 750 \times \left(\frac{\text{MP'}}{800}\right) = 750 \times \left(\frac{\$100 \times (1 + \frac{m}{100})}{800}\right) \]
We set this equal to the target revenue of \$150. \[ 150 = 750 \times \left(\frac{100 \times (1 + \frac{m}{100})}{800}\right) \] \[ 150 = \frac{75000}{800} \times (1 + \frac{m}{100}) \] \[ 150 = 93.75 \times (1 + \frac{m}{100}) \] \[ 1 + \frac{m}{100} = \frac{150}{93.75} = 1.6 \] \[ \frac{m}{100} = 0.6 \implies m = 60% \]
The new markup percentage needs to be 60%.
Part 3: Find the increase in percentage points. The original markup was 20%. The new markup is 60%. \[ \text{Increase} = 60 - 20 = 40 \text{ percentage points} \] Step 3: Final Answer:
The shopkeeper needs to increase his markup from 20% to 60%, which is an increase of 40 percentage points.