After 20% increase in cost per kg of rice, a family can now buy 4kg less rice in rs240.what was the original price per kg of rice? ans(10rs)
240/1.2c = 240/c - 4
thank u steve
To solve this problem, we can follow these steps:
Step 1: Let's assume the original price per kg of rice is 'x' rupees.
Step 2: With a 20% increase in cost, the new price per kg of rice is (x + 0.2x) = 1.2x rupees.
Step 3: Now, let's calculate the amount of rice that can be bought for Rs. 240 with the increased price.
The new cost for 1kg of rice = Rs. 1.2x
So, the amount of rice that can be bought for Rs. 240 is 240 / (1.2x) kg.
Step 4: According to the problem, the new amount of rice bought is 4kg less than the original amount.
Therefore, we have the equation: (240 / (1.2x)) = (Original amount - 4)
Step 5: Simplifying this equation, we get: 240 / (1.2x) = original amount - 4.
Step 6: We can substitute the original amount with x in this equation because we assumed the original price as 'x' in the beginning.
So, the equation becomes: 240 / (1.2x) = x - 4.
Step 7: Now, we can solve this equation to find the value of 'x' which represents the original price per kg of rice.
Let's solve it:
240 / (1.2x) = x - 4
To get rid of the fraction, we can multiply both sides by 1.2x:
(240 / (1.2x)) * 1.2x = (x - 4) * 1.2x
240 = 1.2x^2 - 4.8x
Rearranging the equation to make it quadratic:
1.2x^2 - 4.8x - 240 = 0
Divide the entire equation by 1.2 to simplify:
x^2 - 4x - 200 = 0
Solving this quadratic equation using factoring, completing the square, or using the quadratic formula, we find:
(x - 20)(x + 10) = 0
Since the original price cannot be negative, we take x = 20.
Therefore, the original price per kg of rice was 20 rupees.