Question : A shopkeeper bought a certain number of apples for Rs. 3,600. He sold one-fifth of them at a loss of 10%, one-fourth of the remaining apples at a loss of 5%, and two-thirds of the rest at a profit of 15%. At what price (in Rs.) should he sell the remaining apples to earn a profit of 27% overall?
Option 1: 1,548
Option 2: 1,584
Option 3: 1,845
Option 4: 1,864
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Correct Answer: 1,584
Solution : A shopkeeper bought a certain number of apples for Rs. 3,600. He wants 27% profit overall. So, the overall selling price for the full set must be $\frac{3600 × 127}{100} = 4572$ Let's assume he has 100 apples. An apple costs $\frac{3600}{100} = 36$ He sold one-fifth of them at a loss of 10%. One-fifth of 100 is 20 apples. The selling price of 20 apples is $(\frac{9}{10} × 36 × 20) = 648$ One-fourth of the remaining apples are sold at a loss of 5%. One-fourth of the remaining apples = (100 – 20) × $\frac{1}{4} = 20$ The selling price of the next 20 apples is $(\frac{95}{100} × 36 × 20) = 684$ Two-thirds of the rest are sold at a profit of 15%. Two-thirds of the rest is $(100 – 20 – 20) × \frac{2}{3} = 40$. The selling price of the next 40 apples is $(\frac{115}{100} × 36 × 40) = 1656$ So, to make a 27% profit overall, he needs to sell the rest of the apples at $[4572 – (648 + 684 + 1656)] = 4572 – 2988 = Rs. 1584$ Hence, the correct answer is 1,584.
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