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Four real estate brokers (A, B, C and D) joins together to form a business firm so they get more customers with a condition that for every sale the firm obtains 2% of commission is charged. The commission will be shared such that the person who brought in the customer will get 40% of the commission and others get 20% each. If the ratio of sales made by the brokers are in the ratio 5 ∶ 7 ∶ 6 ∶ 7 respectively. If the commission received by B, C and D is more than the commission received by A by Rs 176781.8, what is the total sales made by the company? (in rupees)

Four real estate brokers (A, B, C and D) joins together to form a business firm so they get more customers with a condition that for every sale the firm obtains 2% of commission is charged. The commission will be shared such that the person who brought in the customer will get 40% of the commission and others get 20% each. If the ratio of sales made by the brokers are in the ratio 5 ∶ 7 ∶ 6 ∶ 7 respectively. If the commission received by B, C and D is more than the commission received by A by Rs 176781.8, what is the total sales made by the company? (in rupees) Correct Answer 339965

Let the ratio of sales brought be 5a, 7a, 6a and 7a

Commission obtained by A = 40% of sales by first broker + 20% of remaining sales

⇒ 40/100 × 5a + 20/100 × (7a + 6a + 7a)

⇒ 2a + 4a = 6a

Commission obtained by B = 40/100 × 7a + 20/100 × (5a + 6a + 7a)

⇒ 2.8a + 3.6a = 6.4a

Commission obtained by C = 40/100 × 6a + 20/100 × (5a + 7a + 7a)

⇒ 2.4a + 3.8a = 6.2a

Commission obtained by D = 40/100 × 7a + 20/100 × (5a + 6a + 7a)

⇒ 2.8a + 3.6a = 6.4a

Commission of B + C + D – Commission of A = 176781.8

6.4a + 6.2a + 6.4a – 6a = 176781.8

⇒ 13a = 176781.8

∴ a = 13598.6

Total sales = 5a + 7a + 6a + 7a

⇒ 25a = 25 × 13598.6 = Rs. 339965

∴ The total sales made by the company Rs. 339965.

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