1.

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

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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