| A piece of string is 40 cm long. It is cut into three pieces. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 cm shorter than the longest piece. The length of the shortest piece is |
A) 27 cm
B) 1 cm
C) 4 cm
D) 9 cm
Correct Answer: C
Solution :
| Let the longest piece be x cm, middle sized piece be y cm and shortest piece be z cm long, |
| Then, \[x+y+z=40\] ...(i) |
| \[x=3y\] ... (ii) |
| \[z=x-23\] ... (iii) |
| On substituting the values of x and z in Eq. (I), we get |
| \[3y+y+x-23=40\] |
| \[\Rightarrow \] \[3y+y+3y-23=40\]\[\Rightarrow \]\[7y=40+23\] |
| \[\Rightarrow \]\[y=9\,\,cm\]\[\Rightarrow \]\[x=3\times 9=27\,\,cm\] |
| \[\therefore \]Required shortest piece \[=z=27-23=4\,\,cm\] |
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