Question

A piece of rope is cut into 2 parts in the ratio of 3:5. The longer part is 16cm longer than the shorter part. Find the length of the original rope and length of the longer part of the rope?

Answer 1

Step-by-step explanation:

Let the length of original rope be x.

Total number of parts = 5 + 3 = 8

=> Length of longer part = 5/8 x

Length of shorter part = 3/8 x

According to the question,

$\frac{5}{8} x - \frac{3}{8} x = 16 \\ = > \frac{5 - 3}{8} x = 16 \\ = > \frac{2}{8} x = 16 \\ = > x = 16 \times \frac{8}{2} \\ = > x = 8 \times 8 = 64 \: cm$

Therefore, actual length of rope is 64 cm.

Thus, longer part of rope:

= 5/8 x

= 5/8 × 64

= 5 × 8

= 40 cm

Therefore, the longer part of the rope is 40 cm.

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