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Xavier Aptitude Test 2011 Paper

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Question : 40 of 101

Marks: +1, -0

Rakhal is looking for a field where he can graze his cow. He finds a local farmer, Gopal, who agrees to rent his 2 field to Rakhal for Rs.1000 a year. Rakhal finds a post in the field and ties his cow to the post with a 25 feet rope . After some months, Gopal tells Rakhal that he will build a shed with four walls on the field with the post as one of the corner posts. The shed would be 15 feet by 10 feet. Rakhal agrees but he realizes that this arrangement would reduce the available area for grazing. What should be the modified rent to compensate for this loss grazing area if Rakhal has to keep the cow tied to the same post with the same rope ?

Rs.800
Rs. 880
Rs. 888
Rs. 930
None of the above

Solution:

(b)

For 3 quadrants there would be no difference as all of the field here is available for grazing.

For the IV one area for grazing before shed was made

=\frac{\pi\times 25^{2}}{4}

after shed is made

=\frac{\pi}{4}(10^{2}+15^{2})

Fraction of the total area over which cow can graze

=\frac{10^{2}+15^{2}}{25^{2}}=\frac{2^{2}+3^{2}}{5^{2}}=\frac{13}{25}

\therefore

Rent for the quadrant would be

\frac{13}{25}(250)=130

\therefore

The new rent should be

3 \times \frac{1000}{4}+130=880

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