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:
- Let the third number be CCC.
- 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−100pC=(1−100p)C.
- 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−100qC=(1−100q)C.
- 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.