The price of an item is increased by 15% and then by 20%. Now the price of the item is decreased so that the overall effective increment in the price is 5%. The price is decreased approximately by ____%.
23.91
Let the original price be \(100\).
After a 15% increase, the price becomes \(100 \times 1.15 = 115\).
After a further 20% increase, the price becomes \(115 \times 1.20 = 138\).
The final price must reflect an overall 5% increase, so the final price is \(100 \times 1.05 = 105\).
Let the required decrease be \(x\%\). Then \(138 \times (1 - \frac{x}{100}) = 105\).
So \(1 - \frac{x}{100} = \frac{105}{138} = 0.7609\), giving \(\frac{x}{100} = 0.2391\).
Hence, \(x = 23.91\%\).
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X sells goods to Y at a profit of 20 percent and Y sells the same goods to Z at a profit of 50 percent. If the cost price for Z is Rs 9000, then what is the cost of the goods for X?
