PSLEA rope was first cut into two pieces in the ratio 3 : 2. The longer piece was then cut into two pieces in the ratio 3 : 1. Among the three pieces, the length of the shortest piece was 120 cm. What was the length of the rope before it was first cut?
Longer piece
|
Shorter piece
|
Total
|
3x4 = 12 u
|
2x4 = 8 u |
5x4= 20 u |
Longer part |
Shorter part |
|
|
3x3 = 9 u |
1x3 = 3 u |
8 u |
20 u |
3 + 1 = 4
The longer piece of the rope is the combined repeated identity.
LCM of 4 and 3 = 12
Length of the shortest piece = 3 u
3 u = 120
1 u = 120 ÷ 3 = 40
Length of the rope
= 20 u
= 20 x 40
= 800 cm
Answer(s): 800 cm