Latest TCS Aptitude Question SOLUTION: Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is: (1) 1050 sq.m (2)

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Four horses are tethered at 4 corners of a square field of side 70 metres so that they just cannot reach one another. The area left ungrazed by the horses is:

(1) 1050 sq.m (2) 3850 sq.m
(3) 950 sq.m (4) 1075 sq.m

Asked In TCS Ram (9 years ago)

Solved BHASKAR MANDAL Read Solution (5)

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BHASKAR MANDAL  (9 years ago) Best Solution

area ungrazed is given by
total area - 4*area grazed by each horse
= 70*70 - 4*(90/360)*pi*(70/2)^2
as the angle made by the horse is 90 degree, so applying the area of the sector,= theta/360*pi*radius^2 above
= 70*70 - pi*(70/2)*(70/2)
= 70*70 { 1- pi/4}
= 70*70{6/(7*4)} , expanding pi = 22/7
= (70*70*6) / (7*4)
= 1050 sq m
so answer is option 1

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neha kumari  (9 years ago)

Area grazed by one horse=(90/360) pi (35)^2=962.5m^2
total area grazed by 4 horses=962.5*4=3850 m^2
Area left=1050 m^2

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Aastha Trivedi  (9 years ago)

Area of each sector = (π*r^2*angle)/360°
On solving for 4 sectors = 4*(π*35^2*90°)/360°
On solving area of 4 sectors = 3850
Reqd. Area = (70*70)-3850 =1050 sq.m

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M.Hariprasad  (7 years ago)

each horse can graze 1/4 th of a circe i.e.., pi r^2 /2
and 4 horses total multiplied by 4 3850
area of square 70 ^2 =4900
ungrazed area 4900-3850=1050

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Ankit Abinash  (7 years ago)

Area of circle= Pi x r^2
in given case there are 4 quadrants at the each corner of the square. so it is equal to a circle.So we can make use of this formula directly.
So the required area will be = total area - area of circle= (70*70) - (Pi*35*35)= 4900-3850=1050sq.m

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