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Profit and loss

Finance and economics, grade 10 (3 units) Lesson 8 of 15Learning

Profit and loss

Cost, revenue and profit

A business’s profit is its revenue minus its cost.

  • The cost – what the business paid: here, the buying price of the goods.
  • The revenue – what the business received: the selling price of one unit times the number of units it sold.

Maya sells phone cases at a stall in the market.
She buys each case for 25 ₪, and sells it for 40 ₪.
This week she sold 60 cases.

  • The cost: 60×25=1500\displaystyle {60\times25}={1500} ₪.
  • The revenue: 60×40=2400\displaystyle {60\times40}={2400} ₪.
  • The profit: 2400−1500=900\displaystyle {2400-1500}={900} ₪ – and on each case 40−25=15\displaystyle {40-25}={15} ₪.

When s\displaystyle s is the selling price of one unit, x\displaystyle x the number of units, R\displaystyle R the revenue and C\displaystyle C the cost:

R=s⋅x\displaystyle R=s\cdot x
P=R−C\displaystyle P=R-C
Loss

When the revenue is less than the cost, the profit is negative – and the business makes a loss.

At the end of the season Maya sells the cases that are left for 20 ₪ each.

  • On each case: 20−25=−5\displaystyle {20-25}={-5} ₪ – a loss of 5 ₪.
  • On 30 cases: 30×20−30×25=600−750=−150\displaystyle {30\times20-30\times25}={600-750}={-150} – a loss of 150 ₪.

A business sometimes sells at a loss on purpose: 20 ₪ for a case is better than nothing for it.

The profit percent

The profit percent is the profit as a part of the cost.

  • On one case Maya makes 15 ₪, and it costs her 25 ₪: 1525=60%\displaystyle {\frac{15}{25}}={60\%}.
  • A 60% profit means: the selling price is 100%+60%=160%\displaystyle {100\%+60\%}={160\%} of the cost. Check: 1.6×25=40\displaystyle {1.6\times25}={40}.
  • The loss percent is worked out in the same way: selling for 20 ₪, 525=20%\displaystyle {\frac{5}{25}}={20\%} loss.
r%=PC\displaystyle r\%=\frac{P}{C}

The profit percent is out of the cost, not out of the selling price: 1540\displaystyle \frac{15}{40} is another part, not the profit percent.

Exercise 1

Work out the profit percent or the loss percent.

a
Ron bought a bike for 800 ₪, and sold it for 1000 ₪.

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b
    Shira bought a phone for 1200 ₪, and sold it a year later for 900 ₪.

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      c
      A concert’s costs were 30,000 ₪, and the revenue from the tickets 36,000 ₪.

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        The selling price for a wanted profit

        A profit of r%\displaystyle r\% means that the selling price is 100%+r%\displaystyle 100\%+r\% of the cost – one multiplication, as in a rise in percent.

        A shop buys a bottle of olive oil for 60 ₪, and wants a 35% profit on it.

        • The selling price: 1.35×60=81\displaystyle {1.35\times60}={81} ₪.
        • The profit on a bottle: 81−60=21\displaystyle {81-60}={21} ₪, and 2160=35%\displaystyle {\frac{21}{60}}={35\%}.

        And when you know the selling price and the profit percent, the cost is the unknown of an equation: a shop sells a book for 72 ₪ at a 20% profit, so 1.2x=72\displaystyle {1.2x}={72} and x=60\displaystyle {x}={60} ₪.

        Exercise 2

        Work out the selling price.

        a
        A cost of 120 ₪, a 40% profit

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          b
          A cost of 45 ₪, a 20% profit

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            Exercise 3

            A shop sells a watch for 150 ₪, at a 25% profit.
            Write an equation and solve it: how much did the shop pay for the watch?

            Exercise 4

            A trader bought 50 shirts, for 30 ₪ each.
            He sold 40 shirts for 55 ₪ each.
            He sold the 10 shirts that were left in a sale, for 20 ₪ each.

            a
            The cost of all the shirts

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

              b
              The revenue from all the shirts

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                c
                The trader’s profit percent

                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                  Exercise 5

                  A shop bought a device for 100 ₪, and raised the price by 20% to make a profit.
                  At the end of the season it gave a 20% discount on the device.
                  Work out the price after the discount.
                  Did the shop make a profit on the device, or a loss? What percent?

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power