As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for ₹ 1,200…
As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for ₹ 1,200. What was the original price of rice per kg?
₹ 30
₹ 40
₹ 50
₹ 60
Solution
Let the original price be $p$ per kg. Original quantity $= 1200/p$. New price $= 1.25p$. New quantity $= 1200/(1.25p)$. Difference: $\dfrac{1200}{p} - \dfrac{1200}{1.25p} = 6$, i.e. $\dfrac{1200}{p}\left(1 - \dfrac{1}{1.25}\right) = 6$, so $\dfrac{1200}{p} \times 0.2 = 6$, giving $\dfrac{240}{p} = 6$, $p = 40$. The original price was ₹ 40 per kg.