Question

A dishonest seller sells his grocery items using a false weight and thus gains 5% for a kilogram. He uses the weight of approximately ______.

• A. 940.251
• B. 943.123
• C. 948.238
• D. 952.381

Hint:

Set up the gain percent as (1000 - x)/x times 100 equals 5.

Answer 1

The Correct Option is D

To determine the weight used by a dishonest seller who gains 5% by using false weights, we need to calculate the effective weight based on the relationship between actual and false weight. 

Let's denote:

• The actual weight intended for 1 kilogram = 1000 grams.
• The false weight used by the seller = \(x\) grams.

Given that the seller gains a 5% profit using a false weight, the profit percentage can be represented as:

\(\text{Profit Percentage} = \frac{\text{Actual Weight} - \text{False Weight}}{\text{False Weight}} \times 100\%\)

Substitute the known profit percentage:

\(\frac{1000 - x}{x} \times 100\% = 5\%\)

To solve for \(x\), first convert the percentage equation to its decimal form:

\(\frac{1000 - x}{x} = \frac{5}{100}\)

Simplify the equation further:

\(1000 - x = \frac{5}{100} \times x\)

Rearrange to isolate \(x\) on one side:

\(1000 = x + \frac{5}{100} \times x\)

\(1000 = x (1 + \frac{5}{100})\)

\(1000 = x \times \frac{105}{100}\)

Calculate \(x\) by multiplying both sides by \(\frac{100}{105}\):

\(x = 1000 \times \frac{100}{105} = \frac{1000 \times 100}{105}\)

Since \(\frac{1000}{105} \approx 9.52381\), we multiply:

\(x \approx 952.381\) grams.

Thus, the seller uses a weight of approximately 952.381 grams.

Conclusion: The correct answer is 952.381 grams.

Answer 2

Step 1: Set up the relation between the true weight and what he actually gives.
Say the seller hands over only \(x\) grams to the customer but charges for a full 1000 grams (1 kg). His real cost is only for the \(x\) grams he gives, while he collects money as if he gave 1000 grams.

Step 2: Write the gain percent in terms of x.
Gain percent \(= \dfrac{1000 - x}{x} \times 100\). We are told this gain is 5%, so:
\[ \frac{1000-x}{x} \times 100 = 5 \]

Step 3: Solve for x.
\(1000 - x = 0.05x\), so \(1000 = 1.05x\), which gives \(x = \dfrac{1000}{1.05}\). Dividing this out: \(x \approx 952.381\).

Final Answer:
The seller actually hands over about 952.381 grams while charging for a full kilogram.
\[ \boxed{952.381} \]