A person has to procure an object through series of 9 agents. He agree

1.	A person has to procure an object through series of 9 agents. He agrees to pay 2% of the item cost as commission to first agent. For second agent he agrees to pay 5% more commission than he paid to first, for third agent 5% more than the second and so on. What is the total percentage of commission he paid? (Use 1.095 ≈ 1.55)1. 202. 223. 334. 27.55. 25
Answer» Correct Answer - Option 2 : 22 Let the cost of the object be Rs x Commission paid to first agent = 2/100 × x = 0.02x Commission paid to second agent = (100 + 5) /100 × 0.02x = 1.05 × 0.02x Commission paid to third agent = (100 + 5) /100 × 1.05 × 0.02x = 1.05² × 0.02x … Commission paid to ninth agent = 1.05⁸ × 0.02x Total commission paid = 0.02x + 1.05 × 0.02x + 1.05² × 0.02x + … + 1.05⁸ × 0.02x ⇒ 0.02x × (1 + 1.05 + 1.05² + … + 1.05⁸) ⇒ 0.02x × (1.05⁹ – 1) / (1.05 – 1) [∵ Sum of n terms of G.P. = a (rⁿ – 1) / (r – 1)] ⇒ 0.02x × (1.55 – 1) / 0.05 = 0.22x ∴ Commission paid = 0.22x/x × 100 = 22%

A person has to procure an object through series of 9 agents. He agrees to pay 2% of the item cost as commission to first agent. For second agent he agrees to pay 5% more commission than he paid to first, for third agent 5% more than the second and so on. What is the total percentage of commission he paid? (Use 1.095 ≈ 1.55)1. 202. 223. 334. 27.55. 25

Answer» Correct Answer - Option 2 : 22

Let the cost of the object be Rs x

Commission paid to first agent = 2/100 × x = 0.02x

Commission paid to second agent = (100 + 5) /100 × 0.02x = 1.05 × 0.02x

Commission paid to third agent = (100 + 5) /100 × 1.05 × 0.02x = 1.05² × 0.02x …

Commission paid to ninth agent = 1.05⁸ × 0.02x

Total commission paid = 0.02x + 1.05 × 0.02x + 1.05² × 0.02x + … + 1.05⁸ × 0.02x

⇒ 0.02x × (1 + 1.05 + 1.05² + … + 1.05⁸)

⇒ 0.02x × (1.05⁹ – 1) / (1.05 – 1) [∵ Sum of n terms of G.P. = a (rⁿ – 1) / (r – 1)]