PSLEA rope was first cut into two pieces in the ratio 2 : 1. The longer piece was then cut into two pieces in the ratio 4 : 1. Among the three pieces, the length of the longest piece was 288 cm. What was the length of the rope before it was first cut?
Longer piece
|
Shorter piece
|
Total
|
2x5 = 10 u
|
1x5 = 5 u |
3x5= 15 u |
Longer part |
Shorter part |
|
|
4x2 = 8 u |
1x2 = 2 u |
5 u |
15 u |
4 + 1 = 5
The longer piece of the rope is the combined repeated identity.
LCM of 5 and 2 = 10
Length of the longest piece = 8 u
8 u = 288
1 u = 288 ÷ 8 = 36
Length of the rope
= 15 u
= 15 x 36
= 540 cm
Answer(s): 540 cm