Three numbers are in the ratio frac{1}{2}: fr | vedclass

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(D) The given ratio of the three numbers is $\frac{1}{2}: \frac{2}{3}: \frac{3}{4}$.To simplify the ratio,multiply each term by the least common multi

Vedclass · Accepted Answer

$72, 96, 108$

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(D) The given ratio of the three numbers is $\frac{1}{2}: \frac{2}{3}: \frac{3}{4}$.To simplify the ratio,multiply each term by the least common multiple $(LCM)$ of the denominators $(2, 3, 4)$,which is $12$.Ratio $= (\frac{1}{2} 	imes 12) : (\frac{2}{3} 	imes 12) : (\frac{3}{4} 	imes 12) = 6: 8: 9$.Let the numbers be $6x, 8x,$ and $9x$.The greatest number is $9x$ and the smallest number is $6x$.According to the problem,the difference between the greatest and smallest numbers is $36$:$9x - 6x = 36$$3x = 36$$x = 12$.Substituting the value of $x$ back into the expressions:First number $= 6 	imes 12 = 72$.Second number $= 8 	imes 12 = 96$.Third number $= 9 	imes 12 = 108$.Therefore,the numbers are $72, 96, 108$.

Three numbers are in the ratio $\frac{1}{2}: \frac{2}{3}: \frac{3}{4}$. The difference between the greatest and the smallest numbers is $36$. The numbers are:

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