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# [Smart Math] Percentages Problem 14

Here’s and example of a SMART MATH problem for PERCENTAGES. ### Problem

An article is sold at a profit of 20%. If both the cost price and selling price were to be $20 less, the profit made would be 10% more. What is the cost price of the article? 1.$30
2. $40 3.$50
4. $60 5.$70

Let the cost price of the article be $x. Hence selling price = 1.2x Reduced cost price = (x – 20) Reduced selling price = (1.2x – 20) Hence, profit % = $\frac{\left( 1.2x-20 \right)-\left( x-20 \right)\times 100}{\left( x-20 \right)}$ = 20% + 10% = 30% $\therefore \frac{\left( 1.2x-20-x+20 \right)\times 100}{\left( x-20 \right)}=30$ $\therefore 0.2x\times 100=30(x-20)$ $\therefore 10x=600$ $\therefore x=60$ = Cost price (Ans: 4) Estimated Time to arrive at the answer = 60 seconds. ### Using Technique [contentblock id=google-adsense-post] As can be seen that by a reduction in cost price, there is an increase in profit %. The increase in profit % = $\frac{10\times 100}{20}=50$% So, for a 50% increase, there should be a 33.33% reduction in cost price (as explained in the Percentages section of Stuff to Remember) Hence, the original cost price should be such that a reduction of$20 is equivalent to a reduction of 33.33%.
Hence, original cost price = $\frac{20\times 100}{33.33}=60$