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?
The second number must be increased by 100% to equal the first number.
Step-by-step solution
Let the third number be CCC.
For easy calculation, take C=100C=100C=100.
1. Find the two numbers
- First number is 50% less than CCC:
A=100−50% of 100=100−50=50A=100-50%\text{ of }100=100-50=50A=100−50% of 100=100−50=50.
- Second number is 75% less than CCC:
B=100−75% of 100=100−75=25B=100-75%\text{ of }100=100-75=25B=100−75% of 100=100−75=25.
So:
- First number A=50A=50A=50.
- Second number B=25B=25B=25.
2. How much % should the second number be enhanced?
We want to increase BBB so that it becomes equal to AAA.
That is, increase 25 to 50.
Increase needed =50−25=25=50-25=25=50−25=25.
Percentage increase =increaseoriginal value×100=\dfrac{\text{increase}}{\text{original value}}\times 100=original valueincrease×100.
So:
Percentage increase=2525×100=100%.\text{Percentage increase}=\frac{25}{25}\times 100=100%.Percentage increase=2525×100=100%.
Therefore, the second number must be enhanced by 100% to make it equal to the first number.
Quick Scoop (story-style intuition)
Think of the third number as 100 coins.
- The first friend gets 50% less than that, so they hold 50 coins.
- The second friend gets 75% less, so they hold only 25 coins.
Now you ask: “By what percent should the poorer friend’s 25 coins grow so they also end up with 50 coins?” They need 25 more coins , which is the same as what they already have , so that’s a 100% increase.
TL;DR:
To make the second number equal to the first, increase the second number by
100%.
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