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Please solve this math question

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The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) isOption 1: 15360Option 2: 153600Option 3: 30720Option 4: 307200

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The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling along the boundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) isOption 1: 15360Option 2: 153600Option 3: 30720Option 4: 307200

Let the length be Land the breadth be b.Then, according to ques, L/ b =3/2 Now, a man cycles with a speed of 12km/h across the boundary and completes his round in 8 minutes.Therefore, the distance travelled by him in this duration is calculated by this formula. Speed * Time = DistanceTherefore, ( 12 * 8 ) / 60 km/minute = Distance 1.6 * 1000 m/min = Distance 1600 = DistanceNow, this distance is 2(L+ b ) of rectangular park.Therefore (L+ b ) = 1600/2 = 800 m ………………………………………………………………..(i) Now. L/ b = 3/2 Or, (L+ b )/(L- b ) = (3+2)/(3-2) = 5/1 Or, 800/5 m = L- b ( by putting the value of eq. 1) 160 m = L- b ………………………………………………………………… (ii)Now by solving eq (i) and eq. (ii), we getL= 480 m and b= 320 m Now. The area of rectangle is L * b= 480 * 320 = 153600 sq. m Hence the answer is “ option 2 “

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The correct answer is 15360.

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