| If one-fourth of the area of a rectangular plot is \[2700\,{{m}^{2}}\] and the width of that plot is 90 m, what is the ratio between the width and length of the plot? [LIC (ADO) 2015] |
A) 3 : 4
B) 4 : 3
C) 3 : 1
D) 1 : 3
E) 4 : 1
Correct Answer: A
Solution :
| Let the area of the rectangular plot \[=x\,{{m}^{2}}\] |
| Given, \[\frac{1}{4}th\]of the area \[=2700\,{{m}^{2}}\] |
| Then, \[\frac{x}{4}=2700\] |
| \[\therefore \] \[x=10800\,{{m}^{2}}\] |
| \[\text{Width}=90\,m\] |
| Length\[\times \]Width = 10800 \[\Rightarrow \] Length \[\times \] 90 = 10800 |
| \[\therefore \] Length = 120 m |
| Required ratio \[=\frac{\text{Width}}{\text{Length}}=\frac{90}{120}=\frac{3}{4}=3:4\] |
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