Question

# Four numbers are in AP whose sum is 50 and the greatest number is four times the smallest number. Find the greatest number among the four.23 20 26 29

Solution

## The correct option is B 20 Let four numbers in A.P. be a−3d, a−d, a+d and a+3d respectively. Then, a−3d+a−d+a+d+a+3d=50 ⇒4a=50⇒a=252 Also given that the greatest number is four times the smallest number. Hence  a+3d=4(a−3d)⇒a+3d=4(a−3d)⇒a+3d=4a−12d⇒15d=3a⇒a=5d⇒252=5d⇒d=52 ∴ The numbers are (252−3×52),(252−52),(252+52) and (252+3×52), i.e. (252−152),(202),(302) and (402) i.e. 5, 10, 15 and 20

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