Find the fraction which bears the same ratio to 1/27 that 3/7 does to 5/9.

5/9

1/35

45/7

7/45

Solution

1/35

Let the required fraction be x.
According to the question,
$straight x space colon 1 over 27 space equals space 3 over 7 space colon thin space 5 over 9$
$rightwards double arrow space space straight x space cross times space 5 over 9 space equals space 1 over 27 cross times 3 over 7 space equals 1 over 63 rightwards double arrow space space straight x space equals space 1 over 63 cross times space 9 over 5 space equals space 1 over 35$