A shopkeeper sold certain articles at 380 after giving a discount of 5 percent. If the discount is not given he would have been gain 20 percent. What is the cost price of the articles (approx.)a)332b)333c)334d)335e)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
Selling price after a 5% discount = $380
If no discount is given, the shopkeeper would have a 20% gain.

To find:
The cost price of the articles.

Let's assume the cost price of the articles is 'x'.

Calculation:
1. Selling price after a 5% discount = $380
Let's calculate the selling price without any discount first.
Selling price without discount = $\frac{100}{100-5} imes 380$
Selling price without discount = $\frac{100}{95} imes 380$
Selling price without discount = $\frac{38000}{95}$
Selling price without discount = $400$

2. If no discount is given, the shopkeeper would have a 20% gain.
Let's calculate the selling price with a 20% gain.
Selling price with 20% gain = $\frac{120}{100} imes x$
Selling price with 20% gain = $\frac{6}{5} imes x$

Based on the given information, we can set up the equation:
$\frac{6}{5} imes x = 400$

Solving the equation:
$x = \frac{400 imes 5}{6}$
$x = \frac{2000}{6}$
$x = 333.33$

Therefore, the cost price of the articles (approx.) is 333.33, which is closest to option 'B' (333).

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