Question

Q.15 - The sum of the three number is 68.If the ratio of the first to
second is 3:2 and that of the second to the third is 5:3 , then the
second number is​

Answer 1

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

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$\large{ \sf{ \frac{680}{31} }}$

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• Sum of three numbers is 68.
• Ratio of 1st to 2nd= 3:2
• Ratio of 2nd to 3rd= 5:3

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• Second number.

$\large{ \sf{\bullet{ \: \: \: let \: the \: no.s \: be \: a \: b \: and \: c}}} \\ \\ \large{ \sf{ \star{ then \: \: \: \: a + b + c = 68}}}\: \\ \\ \large{ \sf{ \bold{ \red{ \underline{according \: to \: question...}}}}} \\ \\ \large{ \sf{ \mapsto{ \green{ \underline{a:b = 3:2}}}}} \\ \\ \large{ \sf{ \diamond{let \: a \: and \: b \: be \: 3x \: and \: 2x}}} \\ \\ \large{ \sf{ \mapsto{ \: then \: \: 3x \: + 2x \: + c \: = 68}}} \\ \\ \large{ \sf{ \mapsto{5x + c = 68}}} \\ \\ \large{ \sf{ \mapsto{c = 68 - 5x}}} \\ \\ \large{ \sf{ \mapsto{ \green{ \underline{b:c = 5:3}}}}} \\ \\ \large{ \sf{ \mapsto{ \frac{2x}{68 - 5x} = \frac{5}{3} }}} \\ \\ \large{ \red{ \sf{ \underline{ \diamond{ \: cross \: multiplying}}}}} \\ \\ \large{ \sf{ \mapsto{5(68 - 5x) = 6x}}} \\ \\ \large{ \sf{ \mapsto{340 - 25x = 6x}}} \\ \\ \large{ \sf{ \mapsto{31x = 340}}} \\ \\ \large{ \sf{ \mapsto{x = \frac{340}{31} }}} \\ \\ \large{ \boxed{ \red{ \sf{ \implies{second \: no. = 2x = \frac{680}{31} }}}}}$

$\large{ \sf{ \star{ \pink{required \: answer \: is \: \frac{680}{31} }}}}$