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A:B = 3:5 and B:C = 10:13, what is A:B:C ?

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An Intiative by Sri Chaitanya

6:10:13

12:14:5

10:7:6

3:5:4

answer is A.

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Detailed Solution

Given, A:B = 3:5 and B:C = 10:13.
So,

\frac{A}{B} = \frac{3}{5}

\Rightarrow 5 A = 3 B

\Rightarrow A = \frac{3}{5} B

\frac{B}{C} = \frac{10}{13}

\Rightarrow 13 B = 10 C

\Rightarrow C = \frac{13}{10} B

Therefore, A:B:C =

\frac{3}{5} B : B : \frac{13}{10} B

.
Cancel B since it is a common multiple.
A:B:C =

\frac{3}{5} : 1 : \frac{13}{10}

A:B:C = 50(

\frac{3}{5} : 1 : \frac{13}{10}

)
A:B:C = 30:50:65
A:B:C = 6:10:13
Therefore, option 1 is correct.

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