Due to a reduction in price by 33.33%, a man gets 25 extra apples. If he spends 75 Rs, what is the reduced price per apple?
original cost per apple ---- x
reduced cost per apple = (2/3)x = 2x/3
75/(2x/3) - 75/x = 25
225/(2x) - 75/x = 25
times 2x
225 - 150 = 50x
50x= 75
x = 75/50 = 1.5
The original price is 1.5 and the reduced price is (2/3)(1.5) = 1
check:
at 1.5 Rs, he can buy 75/1.5 or 50 apples
at 1 RS, he can buy 75/1 or 75 apples, which is 25 apples more.
My answer is correct.
isn't there any short method to calculate it's answer
To find the reduced price per apple, we need to determine the original price of the apples and then calculate the reduced price.
Let's assume the original price per apple is x Rs.
Given that the price is reduced by 33.33%, the reduced price per apple can be calculated using the formula:
Reduced price = Original price - (Original price * Reduction percentage)
So, the reduced price per apple is x - (x * 33.33 / 100) = (3 * x - x * 33.33) / 100 = (3 * x - x * 33.33) / 100 = (100 * x - x * 33.33) / 100 = (100x - 33.33x) / 100 = 66.67x / 100 = 0.6667x
Given that the man gets 25 extra apples, we can set up the following equation:
25 = Original Quantity - Reduced Quantity
Since the original price per apple is x Rs, the original quantity can be calculated by dividing the total amount spent by the original price per apple:
Original Quantity = Total Amount Spent / Original price per apple = 75 Rs / x Rs = 75 / x
The reduced quantity can be calculated by dividing the total amount spent by the reduced price per apple:
Reduced Quantity = Total Amount Spent / Reduced price per apple = 75 Rs / (0.6667x) Rs = 112.5 / x
From the equation 25 = Original Quantity - Reduced Quantity, we can substitute the values:
25 = 75 / x - 112.5 / x
Multiplying both sides by x to remove the denominator:
25x = 75 - 112.5
25x = -37.5
Dividing both sides by 25:
x = -37.5 / 25
x = -1.5
Since a negative price doesn't make sense, there may be an error in the given information or calculation.
To find the reduced price per apple, we need to determine the initial price per apple and apply the reduction percentage.
Let's assume the initial price per apple is 'P' Rs. After the reduction of 33.33%, the price per apple becomes:
Reduced price per apple = P - (33.33/100) * P
= P - (1/3) * P
= (2/3) * P
Now, we know that the man gets 25 extra apples when he spends 75 Rs. This means that the total cost of the apples after the reduction is 75 Rs + (25 * Reduced price per apple) Rs.
Therefore, (2/3) * P = (75 Rs + 25 * Reduced price per apple) Rs
Let's solve this equation to find the reduced price per apple:
(2/3) * P = 75 + 25 * (2/3) * P
Multiplying through by 3 to clear the fraction:
2P = 225 + 50P
50P - 2P = 225
48P = 225
P = 225 / 48
P ≈ 4.69 Rs
So, the initial price per apple was approximately 4.69 Rs, and the reduced price per apple after the 33.33% reduction is:
Reduced price per apple ≈ (2/3) * 4.69
≈ 3.13 Rs
Therefore, the reduced price per apple is approximately 3.13 Rs.