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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.


  1. 23

  2. 20

  3. 26

  4. 29


Solution

The correct option is B

20


Let four numbers in A.P. be a3d, ad, a+d and a+3d respectively.
Then, a3d+ad+a+d+a+3d=50
4a=50a=252
Also given that the greatest number is four times the smallest number.
Hence  a+3d=4(a3d)a+3d=4(a3d)a+3d=4a12d15d=3aa=5d252=5dd=52
The numbers are
(2523×52),(25252),(252+52) and (252+3×52),
i.e. (252152),(202),(302) and (402)
i.e. 5, 10, 15 and 20
 

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