Percentage Problem?

[Atul Kumar]

How could correct answer be 24%

"The output of a factory was increased by 10% to keep with rising demand. To handle holiday rush, this new output was increased by 20%. Approx. what percent would the putput now have to decrease in order to restore the original output? (PR 2007-2008 edition;page#70)?"

TIA,

Atul Kumar

[ratindasgupta]

well final output has become 132%. So if 132 has to reduce to 100, it has to go down to hundred it has to reduce by 32/132*100, ie approx 24.2%

[ldoolitt]

Basically what the above poster said. Say the original sales value is 100. When you multiply that 100 by the first sales increase, the second sales increase and then the final sales decrease you should get back to 100.

100 * I1 * I2 * D1 = 100
I1 * I2 * D1 = 1
1.10 * 1.20 * D1 = 1
D1 = 1/(1.10 * 1.20) = 100/132 = .76

[Gunjan99]

Let 100 be the initial o/p of company.
after 10% increase o/p will be (10/100 * 100 + 100) =110
afte 20% increse
o/p will be (20% of 110 + 110) ie 22+110 = 132.

now to restore the original o/p ie 100..
it has to go down to hundred it has to reduce by 32/132*100, ie approx 24.2%