PSLEA rope was first cut into two pieces in the ratio 4 : 3. The longer piece was then cut into two pieces in the ratio 2 : 1. Among the three pieces, the length of the shortest piece was 96 cm. What was the length of the rope before it was first cut?
Longer piece
|
Shorter piece
|
Total
|
4x3 = 12 u
|
3x3 = 9 u |
7x3= 21 u |
Longer part |
Shorter part |
|
|
2x4 = 8 u |
1x4 = 4 u |
9 u |
21 u |
2 + 1 = 3
The longer piece of the rope is the combined repeated identity.
LCM of 3 and 4 = 12
Length of the shortest piece = 4 u
4 u = 96
1 u = 96 ÷ 4 = 24
Length of the rope
= 21 u
= 21 x 24
= 504 cm
Answer(s): 504 cm