PSLEA wire was first cut into two pieces in the ratio 5 : 4. 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 140 cm. What was the length of the wire before it was first cut?
Longer piece
|
Shorter piece
|
Total
|
5x4 = 20 u
|
4x4 = 16 u |
9x4= 36 u |
Longer part |
Shorter part |
|
|
3x5 = 15 u |
1x5 = 5 u |
16 u |
36 u |
3 + 1 = 4
The longer piece of the wire is the combined repeated identity.
LCM of 4 and 5 = 20
Length of the shortest piece = 5 u
5 u = 140
1 u = 140 ÷ 5 = 28
Length of the wire
= 36 u
= 36 x 28
= 1008 cm
Answer(s): 1008 cm