MathematicsAn annual sports day of a school, in the rectangular play-ground ABCD, lines have been drawn with lime powder at a distance of 1 m   each. 100   plastic cones have been placed at a distance of 1 m   each along AD. Niharika runs 1 20   th the distance AD on the 2nd line and posts a red flag. Preet runs 1 25  th the distance AD on the 8th line and posts a yellow flag. What is the difference in distance between the two flags?

An annual sports day of a school, in the rectangular play-ground ABCD, lines have been drawn with lime powder at a distance of 1 m   each. 100   plastic cones have been placed at a distance of 1 m   each along AD. Niharika runs 1 20   th the distance AD on the 2nd line and posts a red flag. Preet runs 1 25  th the distance AD on the 8th line and posts a yellow flag. What is the difference in distance between the two flags?


  1. A
    37 units
  2. B
    37   units
  3. C
    45 units
  4. D
    3 5   units 

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    Solution:

    Given that, 100   plastic cones have been placed at a distance of 1 m  each along AD.
    We shall find the difference in size of two flags.
    Lines have been drawn with lime powder at a distance of 1 m each.
    100   plastic cones have been placed at a distance of 1  m each along Niharika runs 1 20 th   the distance AD on the 2nd   line and posts a red flag.
    Preet runs 1 25 th   the distance AD on the 8th line and posts a yellow flag.
    Coordinate of Niharikas flag=(2, 1 20 ×100) =(2,5) Coordinate of Preets flag=(8, 1 25 ×100) =(8,4)  
    The distance formula between two points ( x 1 , y 1 ),( x 2 , y 2 )   is given by,
    x 2 x 1 2 + y 2 y 1 2  
    Here,
    ( x 1 , y 1 )=(2,5) ( x 2 , y 2 )=(8,4)  
    The distance between the points (2, 5) and (8, 4) is given by,
    d= (82) 2 +(4 5 2 ) = 6 2 + (1) 2 = 36+1 = 37 units  
    Distance between Niharika's flag and Preet's flag is 37 units  .
    Hence, option 2) is correct.
     
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