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Quantity B: Fifth term of a G.P. is 2. Then 75% of the product of its first nine terms:1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B |
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Answer» First we will find QUANTITY A, Quantity A: Let the number be ‘x’. 85% of the number = 85% of x = 0.85x According to the question, 0.85x + 95 = x – 20 ⇒ 0.15x = 115 ⇒ x = 115/0.15 = 766.6 ∴ The number is 766.6 Now, Quantity B: We know that for a G.P.- nth term = arn-1 Where, a = 1st term, r = common ratio ⇒ 5th term = t5 = ar4 = 2 Product of its first NINE terms = (a) × (ar) × (ar2) ×………× (ar8) = a9 r1 + 2 + 3 + ….+ 8 = a9 r36 = (ar4)9 = 29 = 512 75% of the product of its first nine terms = (75/100) × 512 = 384 ∴ Quantity A > Quantity B |
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