Question

The ratio of the length of Rope $A$ to the length of Rope $B$ is $3:4$.The ratio of the length of Rope $C$ to the length of Rope $B$ is $7:6$. If the length of the longest rope is $84cm$, find the total length of the four ropes.

• A. $210cm$
• B. $225cm$
• C. $240cm$
• D. $200cm$

Answer 1

The correct option is A $210cm$

Let the length of Rope A be 3x and length of Rope B be 4x.
Given than $\frac{LengthofRopeC}{LengthofRopeB}=\frac{7}{6}$
$\Rightarrow$ Length of Rope C
$\frac{7}{6}\times LengthofRopeB=\frac{7}{6}\times 4x=\frac{14x}{3}$
$\therefore$ Rope C is the longest rope.
$\frac{14x}{3}=84\Rightarrow x=18$
$\therefore$ Length of Rope A = 3 X 18=54 cm
Length of Rope B = 4 X 18 = 72 cm
hence, total length of three ropes = 84+ 54+ 72= 210 cm