PSLEA string was first cut into two pieces in the ratio 4 : 3. 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 224 cm. What was the length of the string before it was first cut?
Longer piece
|
Shorter piece
|
Total
|
4x5 = 20 u
|
3x5 = 15 u |
7x5= 35 u |
Longer part |
Shorter part |
|
|
4x4 = 16 u |
1x4 = 4 u |
15 u |
35 u |
4 + 1 = 5
The longer piece of the string is the combined repeated identity.
LCM of 5 and 4 = 20
Length of the longest piece = 16 u
16 u = 224
1 u = 224 ÷ 16 = 14
Length of the string
= 35 u
= 35 x 14
= 490 cm
Answer(s): 490 cm