A man sells an article at a profit of 19%. If the had bought it at 30%

1.	A man sells an article at a profit of 19%. If the had bought it at 30% less and sold it for Rs.42 less, he would have gained 50%. Find the cost price of the article1). Rs. 2102). Rs. 703). Rs. 1404). Rs. 300
Answer» Let the cost price of the article be C. Initial selling price = $(\left( {1 + \frac{{19}}{{100}}} \right)C = 1.19 C)$ If the cost price had been 30% less, we have Revised cost price = $(C\left( {1 - \frac{{30}}{{100}}} \right) = \frac{7}{10}C = 0.7 C)$ Revised selling price = 1.19C - 42 New profit percentage = $(\frac{{\left( {1.19C - 42} \right) - 0.7C}}{{0.7C}} = \frac{{0.49C - 10.5}}{{0.7C}} )$ GIVEN, this figure is 50%. $(\Rightarrow \frac{{0.49C - 42}}{{0.7C}} = \frac{{50}}{{100}})$ ⇒ 49 C – 4200 = 35 C ⇒ 14 C = 4200 ⇒ C = 300

A man sells an article at a profit of 19%. If the had bought it at 30% less and sold it for Rs.42 less, he would have gained 50%. Find the cost price of the article1). Rs. 2102). Rs. 703). Rs. 1404). Rs. 300

Answer»

Let the cost price of the article be C.

Initial selling price = $(\left( {1 + \frac{{19}}{{100}}} \right)C = 1.19 C)$

If the cost price had been 30% less, we have

Revised cost price = $(C\left( {1 - \frac{{30}}{{100}}} \right) = \frac{7}{10}C = 0.7 C)$

Revised selling price = 1.19C - 42

New profit percentage = $(\frac{{\left( {1.19C - 42} \right) - 0.7C}}{{0.7C}} = \frac{{0.49C - 10.5}}{{0.7C}} )$

GIVEN, this figure is 50%.

$(\Rightarrow \frac{{0.49C - 42}}{{0.7C}} = \frac{{50}}{{100}})$

⇒ 49 C – 4200 = 35 C

⇒ 14 C = 4200

⇒ C = 300

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