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If third proportional of 12 and 24 be x, then what is the value of x?
45
49
50
48
48
For three numbers in continued proportion (a,b,x), the third proportional is always equal to b2/a. Here, (24├Ч24)/12=24├Ч2=48.
First number a=12, Second number b=24, and let the third proportional be x.
x=ab2тАЛ
For three numbers in continued proportion (a,b,x), the third proportional is always equal to b2/a. Here, (24├Ч24)/12=24├Ч2=48.
Confusing third proportional with mean proportional. The mean proportional of a and b is abтАЛ, whereas the third proportional of a and b is b2/a.
Understand Continued Proportion
Three numbers a, b, and x are in continued proportion if the ratio of the first to the second is equal to the ratio of the second to the third: a:b=b:x.
baтАЛ=xbтАЛ
Substitute the Given Values
Substitute a=12 and b=24 into the proportion equation: 2412тАЛ=x24тАЛ.
2412тАЛ=x24тАЛ
Solve for x
Cross-multiply to solve for x: 12├Чx=24├Ч24, which gives x=12576тАЛ=48.
x=1224├Ч24тАЛ=48
D is correct because the calculated third proportional value of x is 48.
Understanding continued proportions helps in solving problems related to mean proportional, fourth proportional, and geometric progressions in quantitative aptitude.
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