PSLEA thread was first cut into two pieces in the ratio 2 : 1. 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 24 cm. What was the length of the thread before it was first cut?
Longer piece
|
Shorter piece
|
Total
|
2x3 = 6 u
|
1x3 = 3 u |
3x3= 9 u |
Longer part |
Shorter part |
|
|
2x2 = 4 u |
1x2 = 2 u |
3 u |
9 u |
2 + 1 = 3
The longer piece of the thread is the combined repeated identity.
LCM of 3 and 2 = 6
Length of the shortest piece = 2 u
2 u = 24
1 u = 24 ÷ 2 = 12
Length of the thread
= 9 u
= 9 x 12
= 108 cm
Answer(s): 108 cm