Question

If $P:Q=\frac{3}{5}:\frac{5}{7}.Q:R=\frac{3}{4}:\frac{2}{5}$ then what is $P:Q:R$ equal to?

• A. $\frac{3}{5}:\frac{5}{7}:\frac{2}{5}$
• B. $\frac{9}{20}:\frac{15}{28}:\frac{2}{7}$
• C. $\frac{3}{5}:\frac{3}{4}:\frac{2}{5}$
• D. $\frac{3}{5}:\frac{5}{7}:\frac{3}{4}$

Answer 1

The correct option is B $\frac{9}{20}:\frac{15}{28}:\frac{2}{7}$

$P:Q=\frac{3}{5}:\frac{5}{7}=(21:25)\times 3=63:75$
$Q:R=\frac{3}{4}:\frac{2}{5}=(15:8)\times 5=75:40$
$P:Q:R=63:75:40$
Let us check options one by one.
(a) $(\frac{3}{5}:\frac{5}{7}:\frac{2}{5})\times 35[LCMof5,7,5$ is $35]$
$21:25:14$ [not correct]
(b) $(\frac{9}{20}:\frac{15}{28}:\frac{2}{7})\times 140$ [LCM of $20,28,7$ is $140]$
$=63:75:40$
This matches what we obtained above.
Hence option (b) is correct.