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X sends out certain goods to Y, costing ₹1,50,000 at cost plus 25% on the invoice price. Three-fourths of the goods were sold by Y for ₹1,76,000. The commission is 5% up to the invoice value and 10% of any surplus above the invoice value.

What is the amount of commission?

(a) ₹10,100
(b) ₹11,975
(c) ₹10,568.75
(d) ₹9,350

Answer :

To calculate the commission, we first need to understand the scenario provided. Let's break it down step-by-step:

  1. Understanding the Invoice Price:

    The cost price of goods is ₹1,50,000 and they are sent at cost plus 25% on the invoice price. Let the invoice price be 'x'. Hence, we have:

    [tex]\text{Cost price} = x - 0.25x = 0.75x[/tex]

    Therefore, [tex]0.75x = ₹1,50,000[/tex]

    Solving for 'x', we find the invoice price:

    [tex]x = \frac{₹1,50,000}{0.75} = ₹2,00,000[/tex]

  2. Goods Sold Calculation:

    3/4 of the goods were sold, so the value of goods sold according to the invoice price is:

    [tex]\frac{3}{4} \times ₹2,00,000 = ₹1,50,000[/tex]

  3. Calculating Commission:

    • Commission up to invoice value (5%):

      Since all of the 3/4 goods were sold at the invoice value, the first 5% commission is calculated on ₹1,50,000:

      [tex]5\% \text{ of } ₹1,50,000 = \frac{5}{100} \times ₹1,50,000 = ₹7,500[/tex]

    • Additional Sales Surplus (10%):

      The goods were sold for ₹1,76,000 in total.

      Surplus sale value over the invoice value of goods sold is:

      [tex]₹1,76,000 - ₹1,50,000 = ₹26,000[/tex]

      Commission on surplus at 10%:

      [tex]10\% \text{ of } ₹26,000 = \frac{10}{100} \times ₹26,000 = ₹2,600[/tex]

  4. Total Commission Calculation:

    Add both commissions together:

    [tex]₹7,500 + ₹2,600 = ₹10,100[/tex]

Therefore, the correct answer is (a) ₹10,100.

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Rewritten by : Barada