two numbers are 50% and 75% lesser than a third number. by how much percent is the second number to be enhanced to make it equal to the first number?

two numbers are 50% and 75% lesser than a third number. by how much percent is the second number to be enhanced to make it equal to the first number?

2 weeks ago 3
Nature

To find by how much percent the second number should be enhanced to make it equal to the first number, when both are lesser than a third number, follow these steps:

  1. Let the third number be CCC.
  2. The first number AAA is p%p%p% lesser than CCC, so A=C−p100C=(1−p100)CA=C-\frac{p}{100}C=(1-\frac{p}{100})CA=C−100p​C=(1−100p​)C.
  3. The second number BBB is q%q%q% lesser than CCC, so B=C−q100C=(1−q100)CB=C-\frac{q}{100}C=(1-\frac{q}{100})CB=C−100q​C=(1−100q​)C.
  4. The percentage increase required for BBB to equal AAA is calculated by:

Percentage increase=A−BB×100\text{Percentage increase}=\frac{A-B}{B}\times 100Percentage increase=BA−B​×100

For example, if the first number is 50% lesser and the second number is 75% lesser than the third number,

  • A=0.5CA=0.5CA=0.5C,
  • B=0.25CB=0.25CB=0.25C,
  • The increase needed is:

0.5C−0.25C0.25C×100=0.25C0.25C×100=100%\frac{0.5C-0.25C}{0.25C}\times 100=\frac{0.25C}{0.25C}\times 100=100%0.25C0.5C−0.25C​×100=0.25C0.25C​×100=100%

So, the second number needs to be enhanced by 100% to equal the first number when the first is 50% lesser and the second is 75% lesser than the third number.

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