The price of an article is first decreased by 20% and then increased by 30%. if the resulting price is Rs. 416, the original price of the article is.a)Rs. 350b)Rs. 405c)Rs. 400d)Rs. 450Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Given:
- The price of an article is first decreased by 20% and then increased by 30%.
- The resulting price is Rs. 416.

To find:
- The original price of the article.

Step-by-step solution:

Let's assume the original price of the article is 'x'.

Decrease in price:
When the price is decreased by 20%, the new price becomes (x - 20% of x) = (x - 0.2x) = 0.8x.

Increase in price:
When the decreased price is increased by 30%, the new price becomes (0.8x + 30% of 0.8x) = (0.8x + 0.24x) = 1.04x.

According to the given information, the resulting price is Rs. 416, so we have the equation:

1.04x = 416

Solving for x:
Dividing both sides of the equation by 1.04:
(1.04x) / 1.04 = 416 / 1.04
x = 400

Therefore, the original price of the article is Rs. 400.

Answer:
The original price of the article is Rs. 400. (Option c)

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