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# [Smart Math] Percentages Problem 27

Here’s and example of a SMART MATH problem for PERCENTAGES. An item is sold at a profit of 10%. Had it been bought for 10% less and sold for $10 less, the profit would have been 20%. What is the cost price of the item? 1. 100 2. 1000 3. 500 4. 200 5. 50 ### The Usual Method [contentblock id=google-adsense-post] Let the cost price of the article be$‘x’.

Hence selling price = 1.1x

New cost price = 0.9x

New selling price = 1.1x – 10

Hence profit at new selling price on new cost price = $\frac{\left( 1.1x-10 \right)-\left( 0.9x \right)}{0.9x}\times 100=20$ (As given in the question) $\therefore 20x-1000=18x$ $\therefore x=\frac{1000}{2}=500$

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

Note that the new cost price will be 90% of the original cost price. Hence the denominator in the formula to find profit % (Profit % = $\frac{SP-CP}{CP}\times 100$) will be a multiple of 9 (in this case 0.9x)

Also note that since the new percentage profit being 20% – a whole number, the numerator (SPCP) should also be a multiple of 9. Checking the options as follows:

Option New SP New CP Difference Remarks

a.                     110 – 10 = 100            90                    10                    Not a multiple of 9

b.                     1100 – 10 = 1090        900                  190                  Not a multiple of 9

c.                     550 – 10 = 540            450                  90                    Multiple of 9

No need to check further as there cannot be more than one correct answer!

(Ans: 3)

Estimated Time to arrive at the answer = 30 seconds.
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