Question

The lengths of two ropes are in the ratio $7:5$. Find the length of : Shorter rope, if the longer one is $22.5$m.

Answer 1

Solution:
Step : Calculate the length of shorter rope.
Given, ratio of lengths of two rope = $7:5$
And longer rop = $22.5$m
Let the length of shorter rope is $x$ m.
Then,the ratio of length of longer rope to shorter rope = $22.5:x$
According to the given condition,
$\Rightarrow 7:5$ = $22.5:x$
$\Rightarrow 7\times x$ = $22.5\times 5$
$\because$ (Product of extremes = Product of means)
$\Rightarrow 7x$ = $112.5$
$\Rightarrow x$ = $\frac{112.5}{7}$
$\therefore$ $x$ = $16.07m$
Hence, the length of the shorter rope is $16.07$ m.