Commission of an agent varies directly as total sale and incentive varies directly to the excess of sale over Rs 25000. Total earning of an agent including commission and incentive is Rs 3700 when the total sale is Rs 60000. Whereas when the total sale is Rs 80000, his earning is Rs 5100. Find the total earning of the agent when total sale is Rs 100000.

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Solution

$Let the commission of an agent be denoted as C, incentives be denoted as I and the sale be denoted as S . Thus, we have : C α S \Rightarrow C = k_{1} S . . . (1) I α (25000 + Excess sale over Rs 25000) \Rightarrow I = k_{2} (25000 + Excess sale) . . . (2) Total earning = Commission + Incentive s \Rightarrow 3700 = k_{1} \times 60000 + k_{2} \times 35000 . . . (Exce ss sale over Rs 25000 = Rs 35000 and Total sale = Rs 60000) . . . (3) \Rightarrow 5100 = k_{1} \times 80000 + k_{2} \times 55000 . . . (Exce ss sale over Rs 25000 = Rs 55000 and Total sale = Rs 80000) . . . (4) \Rightarrow k_{2} = \frac{5100 - k_{1} \times 80000}{55000} . . . (5) \Rightarrow 3700 = k_{1} \times 60000 + \frac{5100 - k_{1} \times 80000}{55000} \times 35000 (From 5) \Rightarrow 203500 = 55 \times 60000 k_{1} + 35 \times 5100 - 35 k_{1} \times 80000 \Rightarrow 203500 = 3300000 k_{1} + 178500 - 2800000 k_{1} \Rightarrow 25000 = 500000 k_{1} \Rightarrow k_{1} = \frac{1}{20} Taking k_{1} = \frac{1}{20}, we get : \Rightarrow k_{2} = \frac{5100 - \frac{1}{20} \times 80000}{55000} \Rightarrow k_{2} = \frac{1}{50} Now, we will get the total earnings when the total sale is Rs 10000 . Total earnings = Rs (\frac{1}{20} \times 10000 + \frac{1}{50} \times 75000) = Rs (5000 + 1500) = Rs 6500$

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