Question

Two pieces of rope with lengths of $\frac{13}{5}m$ and $\frac{33}{10}m$ are cut from an 11 m long rope. Which among the following options is true?

• A. The length of the cut rope is $51/10m.$
• B. The length of the cut rope is $58/10m.$
• C. The length of the remaining rope is $51/10m.$
• D. The length of the remaining rope is $59/10m.$

Answer 1

The correct option is C The length of the remaining rope is $51/10m.$

Total length of the rope $=11m$
Total cut length
$=\frac{13}{5}m+\frac{33}{10}m$

$=\frac{13\times 2}{5\times 2}m+\frac{33}{10}m=\frac{26+33}{10}m$

$=\frac{59}{10}m$

Hence, the length of the remaining rope
$=11m-\frac{59}{10}m$

$=\frac{110}{10}m-\frac{59}{10}m$

$=\frac{110-59}{10}m$

$=\frac{51}{10}m$