A pianist agreed to perform one concert at a fee 12.5 percent less tha

Question

A pianist agreed to perform one concert at a fee 12.5 percent less than her usual fee and a second concert at a fee 20 percent greater than the first fee. The fee for the second concert was what percent greater than her usual fee?

A. 5%
B. 7.5%
C. 15%
D. 16.25%
E. 32.5%

A. 5% 
B. 7.5% 
C. 15% 
D. 16.25% 
E. 32.5%

Abhishek009 · Answer

Let usual fee be 40

So, The fee for 1st Concert is 35
And ,The fee for 2nd Concert is 42

ie,  \frac{42 - 40}{40}*100  =  5 %,   Answer must be (A)

generis · Answer

If there is successive percent change, we can
  Use multipliers.  Two ways:

(1) Formula for successive percent change

If there are only two successive percent changes, overall percent change can be found with a very simple formula

A + B + \frac{A*B}{100}

A  = first percent change  = -12.5 
 B  = second percent change =  +20

Overall percent change:
 -12.5 + 20 + (\frac{-12.5*20}{100})

-12.5 + 20 + (-\frac{250}{100})

(-12.5+20-2.5) = 5  percent greater than original (because 5 is positive)

(2) Multiply the multipliers: 
 Numbers :(.875*1.2=1.05)

Fractions 
Multiplier for percent decrease:  12.5 =.125=\frac{1}{8} 
 1-\frac{1}{8}=\frac{7}{8}  of usual fee

Multiplier for percent increase:  20=.20=\frac{1}{5} 
 1+\frac{1}{5}=\frac{6}{5}

Multiply the multipliers:
 (\frac{7}{8}*\frac{6}{5})=\frac{21}{20}=1\frac{1}{20}

Subtract 1 to find percent change.
 (1\frac{1}{20}-1)=(\frac{1}{20}*100)=.05*100=5 % greater than original

Answer A

ScottTargetTestPrep · Answer

We can let her usual fee = 1000, so the fee for her first concert was 0.875 x 1000 = 875, and the fee for her second concert was 1.2 x 875 = 1,050. Now we need to determine what percent greater the fee for the second concert was compared to the usual fee.

(1,050 - 1000)/1000 x 100

50/1000 x 100 = 50/10 = 5 percent

Answer: A

A pianist agreed to perform one concert at a fee 12.5 percent less tha

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A pianist agreed to perform one concert at a fee 12.5 percent less tha

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