Xavier Aptitude Test 2013 Paper

Question : 68 of 121

Marks: +1, -0

The central park of the city is 40 metres long and 30 metres wide. The mayor wants to construct two roads of equal width in the park such that the roads intersect each other at right angles and the diagonals of the park are also the diagonals of the small square formed at the intersection of the two roads. Further, the mayor wants that the area of the two roads to be equal to the remaining area of the park. What should be the width of the roads?

10 metres
12.5 metres
14 metres
15 metres
16 metres

Validate

Solution:

(a)

Hence, (x) (40 – x) + (x) (30 – x) + x

^{2}

= 1200 – [(x) (40 – x) + (x) (30 – x) + x

^{2}

]
2 [(x) (40 – x) + (x) (30 – x) + x

^{2}

] = 1200
40x – x

^{2}

+ 30x – x

^{2}

+ x

^{2}

= 600
– x

^{2}

+ 70x – 600 = 0
x

^{2}

– 70x + 600 = 0
(x – 60) (x – 10) = 0
x = 10 or 60.
As x must be less than 30.
∴ x = 10

Go to Question:

Prev Question

Next Question