A man sells an article at 14 % profit. Had he bought it at 14 % less a

1.	A man sells an article at 14 % profit. Had he bought it at 14 % less and sold it for Rs. 1424 less, he would have gained 16%. Find the cost price.1). Rs. 105002). Rs. 100003). Rs. 95004). Rs. 5000
Answer» Let the Cost price be Rs. x ? the article is sold at 14% PROFIT, Selling price = x + (14% of x) = 1.14x Now, in the second case, the article was bought at 14% lesser value than the previous value ∴ Cost price in second case = x – (14% of x) = 0.86x In the second case, the article was sold at a price Rs. 1424 LESS than the previous selling price. ∴ Selling price in second case = 1.14x – 1424 Now, Gain in the second case = (1.14x – 1424) – 0.86x ∴ % gain $(= \frac{{\LEFT( {1.14x - 1424} \right) - 0.86x}}{{0.86x}} \times 100)$ ⇒ $(16\; = \frac{{\left( {1.14x - 1424} \right) - 0.86x}}{{0.86x}} \times 100)$ ⇒ 16 × 0.86x = 100 × (0.28X – 1424) ⇒ 13.76x = 28x – 142400 ⇒ 14.24x = 142400 ⇒ x = 10000 ∴ Cost price of the article is Rs. 10000.

A man sells an article at 14 % profit. Had he bought it at 14 % less and sold it for Rs. 1424 less, he would have gained 16%. Find the cost price.1). Rs. 105002). Rs. 100003). Rs. 95004). Rs. 5000

Answer»

Let the Cost price be Rs. x

? the article is sold at 14% PROFIT,

Selling price = x + (14% of x) = 1.14x

Now, in the second case, the article was bought at 14% lesser value than the previous value

∴ Cost price in second case = x – (14% of x) = 0.86x

In the second case, the article was sold at a price Rs. 1424 LESS than the previous selling price.

∴ Selling price in second case = 1.14x – 1424

Now, Gain in the second case = (1.14x – 1424) – 0.86x

∴ % gain $(= \frac{{\LEFT( {1.14x - 1424} \right) - 0.86x}}{{0.86x}} \times 100)$

⇒ $(16\; = \frac{{\left( {1.14x - 1424} \right) - 0.86x}}{{0.86x}} \times 100)$

⇒ 16 × 0.86x = 100 × (0.28X – 1424)

⇒ 13.76x = 28x – 142400

⇒ 14.24x = 142400

⇒ x = 10000

∴ Cost price of the article is Rs. 10000.