The sum of three numbers is 68. If the ratio | vedclass

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Question

(A) Let the three numbers be $a, b,$ and $c$.Given ratios are $\frac{a}{b} = \frac{2}{3}$ and $\frac{b}{c} = \frac{5}{3}$.To find the combined ratio $

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(A) Let the three numbers be $a, b,$ and $c$.Given ratios are $\frac{a}{b} = \frac{2}{3}$ and $\frac{b}{c} = \frac{5}{3}$.To find the combined ratio $a:b:c$,we make the value of $b$ common in both ratios.Multiply the first ratio by $5$ and the second ratio by $3$:$\frac{a}{b} = \frac{2 	imes 5}{3 	imes 5} = \frac{10}{15}$$\frac{b}{c} = \frac{5 	imes 3}{3 	imes 3} = \frac{15}{9}$Thus,$a:b:c = 10:15:9$.Let the numbers be $10x, 15x,$ and $9x$.The sum of the numbers is $68$,so:$10x + 15x + 9x = 68$$34x = 68$$x = 2$The second number is $15x = 15 	imes 2 = 30$.

The sum of three numbers is $68$. If the ratio between the first and second is $2:3$ and that between the second and third is $5:3$,then the second number is

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