Exams › IBPS PO › Quantitative Aptitude

A path of width \(x\) metres is carved around a rectangular field. If the length of the rectangular field is 3 m more than its breadth, find the value of \(x\). Statement I: There is a square whose side is 2 m more than the breadth of the rectangular field, and the area of the square is 50 m\(^2\) more than the area of the rectangular field. Statement II: The total cost of construction of the path around the rectangular field is Rs. 1920, and the rate of construction of the path is Rs. 40/m\(^2\). Question: Find the value of \(x\).

1. The data in both statements I and II together are necessary to answer the question.
2. The data in statement II alone is sufficient to answer, while the data in statement I alone is not sufficient to answer the question.
3. The data either in statement I alone or in statement II alone are sufficient to answer the question.
4. The data given in both statements I and II together are not sufficient to answer the question.

Correct answer: The data in both statements I and II together are necessary to answer the question.

Solution

Statement I gives a relation between the breadth and the area difference, but not enough to determine the path width uniquely. Statement II gives the area of the path, but without the field dimensions it is still insufficient. Together, they provide enough equations to determine \(x\).

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