The sum of three numbers is 98. If the ratio | vedclass

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(A) Let the three numbers be $x, y,$ and $z$.Given the ratios:$x:y = 2:3$$y:z = 5:8$To combine these ratios,we make the value of $y$ common in both ra

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) Let the three numbers be $x, y,$ and $z$.Given the ratios:$x:y = 2:3$$y:z = 5:8$To combine these ratios,we make the value of $y$ common in both ratios. The least common multiple of $3$ and $5$ is $15$.Multiplying the first ratio by $5$: $x:y = (2 	imes 5) : (3 	imes 5) = 10:15$.Multiplying the second ratio by $3$: $y:z = (5 	imes 3) : (8 	imes 3) = 15:24$.Thus,the combined ratio is $x:y:z = 10:15:24$.The sum of the parts is $10 + 15 + 24 = 49$.Given the sum of the numbers is $98$,the value of one part is $98 / 49 = 2$.The second number $(y)$ corresponds to $15$ parts.Therefore,the second number is $15 	imes 2 = 30$.

The sum of three numbers is $98$. If the ratio between the first and second is $2:3$ and that between the second and the third is $5:8$,then the second number is

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