JAMB 1989 · UME · Q7

If $a : b = 5 : 8$ and $x : y = 25 : 16$ , evaluate $\frac ax : \frac by$ .

Worked solution (try it first)

Write the ratio as a fraction and divide: $\dfrac ax \div \dfrac by = \dfrac ax \times \dfrac yb$
$= \dfrac ab \times \dfrac yx$ .
Put in $\frac ab = \frac58$ and $\frac yx = \frac{16}{25}$ : $\frac58 \times \frac{16}{25} = \frac{80}{200}$
$= \frac25$ .
So $\frac ax : \frac by = 2 : 5$ , option D.