PSLEA wire was first cut into two pieces in the ratio 2 : 1. The longer piece was then cut into two pieces in the ratio 3 : 1. Among the three pieces, the length of the longest piece was 108 cm. What was the length of the wire before it was first cut?
Longer piece
|
Shorter piece
|
Total
|
2x2 = 4 u
|
1x2 = 2 u |
3x2= 6 u |
Longer part |
Shorter part |
|
|
3x1 = 3 u |
1x1 = 1 u |
2 u |
6 u |
3 + 1 = 4
The longer piece of the wire is the combined repeated identity.
LCM of 4 and 2 = 4
Length of the longest piece = 3 u
3 u = 108
1 u = 108 ÷ 3 = 36
Length of the wire
= 6 u
= 6 x 36
= 216 cm
Answer(s): 216 cm