PSLEA string was first cut into two pieces in the ratio 3 : 2. 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 540 cm. What was the length of the string before it was first cut?
Longer piece
|
Shorter piece
|
Total
|
3x5 = 15 u
|
2x5 = 10 u |
5x5= 25 u |
Longer part |
Shorter part |
|
|
4x3 = 12 u |
1x3 = 3 u |
10 u |
25 u |
4 + 1 = 5
The longer piece of the string is the combined repeated identity.
LCM of 5 and 3 = 15
Length of the longest piece = 12 u
12 u = 540
1 u = 540 ÷ 12 = 45
Length of the string
= 25 u
= 25 x 45
= 1125 cm
Answer(s): 1125 cm