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How was 40+18+40+18 arrived at ?
Here is the question:
Neeraj has agreed to mow a lawn, which is a 20 m × 40 m rectangle. He mows it with 1 m wide strip. If Neeraj starts at one corner and mows around the lawn toward the centre, about how many times would he go round before he has mowed half the lawn? (Round off the answer to two decimal digits)
CrackU Solution:
To mow half of lawn is to mow 400 squares of 1m width each. Neeraj mows 40+18+40+18 = 116 squares of 1m width each in 1st round, in 2nd round he mows 38+16+38+16 = 108 squares and in 3rd round, he mows 36+14+36+14 = 100 squares. So, in total, he mows 324 squares; but he needs 400-324 = 76 more.
If he covers the 4th round completely, he mows 92 squares, to cover only 76, he needs to cover 76/92 = 0.826 round.
So in total 3.826 ≈">≈ 3.83 rounds are required.
He starts from the corner and starts mowing along the length i.e. 40 meters. Then he mows along the breadth. But he will not mow at the second corner again (i.e. the corner after which he shifted to the breadth) because he has already mowed it while mowing along the breadth.So he would have to mow 1m less. Now you can take the breadth to be mowed as 19 meters (20 - 1) and then while mowing along the second length take it as 39 meters (40 - 1) because 3rd corner would have been mowed while mowing towards breadth. Or you can think it as, while mowing breadth he will mow for 18 meters only, and he will mow the 3rd corner while mowing the second length i.e. 40 meters. Either way the sum will be 58 meters. And for the last side (i.e. second breadth) he will mow for 18 meters.
