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Question

Three number a, b, c are between 2 and 18 such that their sum is 25, 2, a, b, are in A.P. and b, c, 18 are in G.P. then abc =
  1. 360
  2. 480
  3. 540
  4. 420


Solution

The correct option is B 480
a + b + c = 25
2,a,b in A.P.2+b=2a,b,c 18 in G.P.18b=c2
Eliminating a from (1), (2), 3b + 2c = 48
Eliminating b from (3), (4), c2+12c=288, solving, c = 12, – 24
But c lies between 2 and 18  c=12,b=8,a=5abc=5,8,12=480

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