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Two numbers are in ratio 2:8. If their sum is 40, find the mean proportional between them.
8
12
16
20
8
Since the ratio is 2:8, simplify it to 1:4. The sum 40 is split into 1+4=5 parts. One part is 40/5=8, so the numbers are 1├Ч8=8 and 4├Ч8=32. The mean proportional is 8├Ч32тАЛ=256тАЛ=16.
Two numbers are in ratio 2:8 and their sum is 40.
Mean┬аProportional=a├ЧbтАЛ
Since the ratio is 2:8, simplify it to 1:4. The sum 40 is split into 1+4=5 parts. One part is 40/5=8, so the numbers are 1├Ч8=8 and 4├Ч8=32. The mean proportional is 8├Ч32тАЛ=256тАЛ=16.
Students often fail to simplify the ratio 2:8 to 1:4, or confuse mean proportional with the average (arithmetic mean).
Define the numbers
Let the numbers be 2x and 8x. Given their sum is 40, we write the equation 2x+8x=40.
10x=40тЯ╣x=4
Calculate the individual values
Substitute x=4 back into the expressions for the two numbers.
First┬аnumber=2├Ч4=8,Second┬аnumber=8├Ч4=32
Apply mean proportional formula
The mean proportional M between two numbers a and b is given by M=a├ЧbтАЛ.
M=8├Ч32тАЛ=256тАЛ=16
C is correct because the numbers are 8 and 32, and their mean proportional is 8├Ч32тАЛ=16.
Mean proportional is a specific case of the geometric progression; remember it is the square root of the product, not the simple average.
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