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If Fatima sells 6060 identical toys at a 40%40\% discount on the printed price, then she makes 20%20\% profit. Ten of these toys are destroyed in a fire. While selling the rest, how much discount%\% should be given on the printed price so that she can make the same amount of profit?

Solution

✅ Correct Option: 4

Let's say the printed price of each toy =P= P

When Fatima sells at 40%40\% discount:

  • Selling price per toy =P−0.4P=0.6P= P - 0.4P = 0.6P
  • Total revenue from 6060 toys =60×0.6P=36P= 60 \times 0.6P = 36P

Since she makes 20%20\% profit:

  • Revenue =1.2×= 1.2 \times Cost price
  • 36P=1.2×36P = 1.2 \times Cost price

Cost price =36P1.2=30P= \dfrac{36P}{1.2} = 30P

Profit =36P−30P=6P= 36P - 30P = 6P


After the fire:

  • Toys remaining =60−10=50= 60 - 10 = 50 toys
  • Cost is still 30P30P (she already bought all 6060 toys)
  • She wants the same profit =6P= 6P
  • Total revenue needed =30P+6P=36P= 30P + 6P = 36P

She needs to earn 36P36P by selling 5050 toys.

Revenue per toy needed =36P50=0.72P= \dfrac{36P}{50} = 0.72P

If discount is d%d\%:

  • Selling price =P(1−d100)= P(1 - \dfrac{d}{100})
  • We need: P(1−d100)=0.72PP(1 - \dfrac{d}{100}) = 0.72P
  • 1−d100=0.721 - \dfrac{d}{100} = 0.72
  • d100=0.28\dfrac{d}{100} = 0.28
  • d=28%d = 28\%

Therefore, she should give 28%28\% discount.

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