If two numbers are in the ratio
5
4
:
6
5
, then by what percentage is the first number more or less than the second number?
- A4% less
- B4% more
- C20% less
- D18\frac{2}{11}% \text{ less}
Solution & Step-by-step Explanation
The given ratio of two numbers is:
Ratio=
5
4
:
6
5
To simplify the ratio into integers, multiply both parts by the LCM of denominators 5 and 6, which is 30:
First Number=
5
4
×30=24
Second Number=
6
5
×30=25
The first number (24) is less than the second number (25) by:
Difference=25−24=1
Percentage by which the first number is less than the second number:
Percentage Less=(
25
1
)×100=4%
Thus, the first number is 4% less than the second number.
Ratio=
5
4
:
6
5
To simplify the ratio into integers, multiply both parts by the LCM of denominators 5 and 6, which is 30:
First Number=
5
4
×30=24
Second Number=
6
5
×30=25
The first number (24) is less than the second number (25) by:
Difference=25−24=1
Percentage by which the first number is less than the second number:
Percentage Less=(
25
1
)×100=4%
Thus, the first number is 4% less than the second number.