Geeta sells A \(→\) 20% (Profit) and B \(→\) 10% (Loss) at the same sp. If she increases SP such that A and B still sold at an equal price and profit of 10% made on B, then profit made on A will be?

Question

An iron beam made with rare materials has its market price dependent on the square of its length. The beam broke into two pieces in the ratio of 4 : 9. If it is sold as two separate pieces, what would be the percentage profit or loss compared to its original value?

Answer 1

Let the initial selling price of items \(A\) and \(B\) be \(p\). She profited 20% on \(A\). This implies \(1.2 \times c = p\), so the cost of \(A\) is \(c = \frac{5p}{6}\). She incurred a 10% loss on \(B\). This implies \(0.9 \times c = p\), so the cost of \(B\) is \(c = \frac{10p}{9}\). She then sold both items at a price that yielded a 10% profit on \(B\). The selling price for \(B\) became \(\frac{11}{10} \times \frac{10p}{9} = \frac{11p}{9}\). The profit percentage on \(A\) is calculated as \(\frac{\frac{11p}{9}-\frac{5p}{6}}{\frac{5p}{6}} \times 100\). Simplifying this yields \(46.66\%\), which is approximately \(47\%\). Therefore, the correct option is (B): \(47\%\).

Geeta sells A \(→\) 20% (Profit) and B \(→\) 10% (Loss) at the same sp. If she increases SP such that A and B still sold at an equal price and profit of 10% made on B, then profit made on A will be?

The Correct Option is B

Solution and Explanation

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