Question 16

The height of nineteen people of comic book is in Arithmetic progression. The average height of them is 19 feet. If the tallest is 37 feet. Then what is the weight of the shortest?

Solution

Let the ages of 19 people be = {a, a+d, a+2d, a+3d.....a+18d}
Sum of all 19 ages = $$\dfrac{\ 19}{2}\left\{2a+18d\right\}$$

So , average =$$\ \dfrac{19(a+9d)\ }{19}$$ = a+9d = 19
Given tallest is a+18d = 37
Therefore, d = 2, a = 1.

Hence, the lightest will be 'a' = 1

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