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# [Smart Math] Percentages Problem 25

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

A sells B a piece of furniture for $45,000 at a loss of 10% B sells it to C at a price which would have given A a profit of 20%. What percent does B gain? 1. 50/3 2. 100/3 3. 30/2 4. 50/4 5. 100/4 ### The Usual Method [contentblock id=google-adsense-post] Selling price of A = Cost price of B =$45000

Hence cost price of A = $\frac{45000}{0.9}=50000$

Selling price of A with 20% profit = Selling price of B = 50000 x 1.2 = 60000

Profit of B       = Selling price of B – Cost price of B

= $60,000 –$45,000 = $15,000 Hence profit percent of B = $\frac{15000}{45000}\times 100=\frac{100}{3}$% (Ans: 2) Estimated Time to arrive at the answer = 45 seconds. ### Using Technique [contentblock id=google-adsense-post] Observe that if A’s cost price would have been$100, his selling price with 10% loss would be $90 and his selling price with 20% gain would be$120. Hence gain = 120 – 90 = 30

Selling price of A with 10% loss = Cost price of B = \$90.

Hence Profit %for B = $\frac{30}{90}\times 100=\frac{100}{3}$%

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.
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