A balance of a trader weighs 20% less than It should be. Still the trader mark-up his goods to get the overall profit of 35%. What is mark-up on the cost price?

Options

A. 0.07
B. 0.08
C. 0.09
D. 0.085

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the weight loss
The trader's balance weighs 20% less than it should. This means that if the actual weight is 100%, the trader is effectively using only 80% of the weight.

**Hint:** Remember that a 20% reduction means you are left with 80% of the original amount.

### Step 2: Calculate the effective selling price to cost price ratio
Since the trader is using only 80% of the weight, the ratio of Selling Price (SP) to Cost Price (CP) can be calculated as follows:
- If the CP is 100, then the SP for the 80% weight is effectively 100/80 = 1.25.
- This means the SP is 125% of the CP, or the ratio of SP to CP is 5:4.

**Hint:** The ratio can be derived from the effective weight used, which is 80%.

### Step 3: Calculate the profit from the effective SP
From the ratio of SP to CP (5:4), we can see that the trader is making a profit of:
- Profit = SP - CP = (5/4)CP - CP = (5/4 - 4/4)CP = (1/4)CP.
- This means the trader is making a profit of 25% on the cost price.

**Hint:** Profit percentage can be calculated as (Profit/CP) * 100.

### Step 4: Determine the required overall profit
The trader wants an overall profit of 35%. Since he is already making a profit of 25%, he needs an additional profit of:
- Additional Profit Needed = 35% - 25% = 10%.

**Hint:** To find the additional profit needed, simply subtract the current profit from the desired profit.

### Step 5: Calculate the markup needed to achieve the additional profit
To find out what percentage markup is needed on the cost price to achieve this additional profit:
- The current profit is based on the effective selling price which is 125% of the cost price.
- To achieve a total profit of 35%, we need to find the markup percentage (let's call it B) such that:
- (Current Profit + Markup Profit) / CP = 35%.

Using the formula:
- (25 + B) = 35,
- B = 35 - 25 = 10.

**Hint:** The markup percentage can be found by setting up the equation based on desired profit.

### Step 6: Calculate the percentage of markup on the cost price
To find the percentage markup based on the current selling price:
- The current selling price is 125% of CP.
- The markup needed to achieve an additional profit of 10% on the cost price is:
- Markup Percentage = (Additional Profit / Current Selling Price) * 100.
- Markup Percentage = (10 / 125) * 100 = 8%.

**Hint:** The markup percentage is calculated based on the current selling price to find out how much more needs to be added.

### Final Answer
The markup on the cost price needed to achieve an overall profit of 35% is **8%**.

---