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By 20% decrease in the price of rice, people can buy 10 kg more rice for ₹100. What is the original price of 1 kg of rice?
₹2.50
₹5.00
₹4.50
₹1.50
₹2.50
Use the formula: Price = (Total Amount × Change %) / (Increased Quantity × (100 - Change %)). Here, (100 × 20) / (10 × 80) = 2000 / 800 = 2.5.
Decrease in price = 20%, Quantity increased = 10 kg, Amount spent = ₹100
Original Price=Quantity×(100−Percentage)Amount×Percentage
Use the formula: Price = (Total Amount × Change %) / (Increased Quantity × (100 - Change %)). Here, (100 × 20) / (10 × 80) = 2000 / 800 = 2.5.
Confusing the original price with the reduced price; the denominator must use (100 - 20) = 80 to find the original base price.
Define variables
Let the original price of rice be x. After a 20% decrease, the new price is 0.8x.
New Price=x×(1−0.20)=0.8x
Set up quantity equation
The quantity bought at the original price is x100 and at the new price is 0.8x100. The difference is 10 kg.
0.8x100−x100=10
Solve for x
Simplify the equation: x125−x100=10, which leads to x25=10.
x=1025=2.5
A is correct because the original price of rice is calculated to be ₹2.50 per kg.
This inverse relationship between price and quantity is a classic concept in economics and competitive math; always remember the shortcut formula: New Price=QuantityAmount×Rate.
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