Let the length of the smaller part of the rope be ‘x’ cm
and that of the larger part be ‘y’ cm.
According to the first condition,
total length of the rope is 560 cm.
∴ x + y = 560 …(i)
Twice the length of the smaller part = 2x
rd length of the larger part = 1/3 y
According to the second condition,
2x =\(\frac{1}{3}\) y
∴ 6x = y
∴ 6x – y = 0 ……(ii)
Adding equations (i) and (ii),
∴ x = 80
Substituting x = 80 in equation (ii),
6x – y = 0
∴ 6(80) – y = 0
∴ 480 – y = 0
∴ y = 480
∴ The length of the larger part of the rope is 480 cm.