27. Let d be the distance of the moneygrubber (守財奴) from the mirror, its image is thus at a distance of d behind the mirror. Draw two light rays, one from the top of the image and the other from the feet of the image, to the eye of the moneybrubber. These two lines will cut the wall at two points. Distance between these two point on the wall gives the shortest length of the mirror.
Therefore, the image, the mirror and the eye of the moneygrubber formed two similar triangles. Hence,
L/H = d/2d
where L is the mirror length, H is the height of the image (same as the height of the object)
i.e. L = H/2
Hence, it can be seen that (i) the mirror length is half that of the object (the moneygrubber), and (ii) the mirror length is independent of the distance at which the object is from the mirror. These two results are generally true.
Because the height of the moneygrubber is 20 units, the shortest mirror length with which he can see his body completely is thus 20/2 units = 10 units. Therefore, option B is the correct answer.
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28. With the explanation given above, the shortest length of mirror is independent of the distance the object is from the mirror. Therefore, statement (1) and (2) are correct.
Statement (3) is clearly wrong. When he stands up, his eyes are above the mirror, he won't be able to see the image of his head. You could confirm this by drawing light rays from his eyes to the mirror.