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

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(B) Let the three numbers be $x, y,$ and $z$.Given that $x + y + z = 98$.We are given the ratios $x:y = 2:3$ and $y:z = 5:8$.To find the combined rati

Vedclass · Accepted Answer

$30$

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(B) Let the three numbers be $x, y,$ and $z$.Given that $x + y + z = 98$.We are given the ratios $x:y = 2:3$ and $y:z = 5:8$.To find the combined ratio $x:y:z$,we equate the $y$ term 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 $10 + 15 + 24 = 49$.The second number $y$ is calculated as:$y = \frac{15}{49} 	imes 98 = 15 	imes 2 = 30$.

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

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