Multiple choice

The sum of three numbers in G.P is 70. If the two extrmes be multiplied each by 4 and the mean by 5, the products are in AP. The numbers are

  1. 12, 18, 40

  2. 10, 20, 40

  3. 40, 20, 10

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the three numbers in G.P. be a/r, a, ar. Their sum is 70. When extremes are multiplied by 4 and mean by 5, we get 4a/r, 5a, 4ar. For these to be in A.P., the middle term must equal the average of first and third: 5a = (4a/r + 4ar)/2. Solving with sum=70 gives the numbers 10, 20, 40. Check: 10+20+40=70 and 4×10, 5×20, 4×40 = 40, 100, 160 which is an A.P. with common difference 60.

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