Question

A piece of string $175cm$ in length was cut into two pieces, the ratio of whose length was $5:2.$ Find the length of each piece.

Answer 1

Let the common multiple of the given ratio of the lengths of the two pieces be $x.$

Let the lengths of the first and second parts be $5xcm$ and $2xcm,$ respectively.

According to the question, $5x+2x=175$

$\Rightarrow 7x=175$

$\Rightarrow x=\frac{175}{7}=25$

Thus, we have:

Length of the first part $=5\times 25=125cm$

Length of the second part $=2\times 25=50cm$