a shopkeeper bought some eggs at rupees 3 each.20 of them were broken while the rest were sold at 4 rupees each.if he made a profit of 20%,find how many eggs he bought
number of eggs bought --- x
number of eggs sold ----- x-20
4(x-20)/(3x) = 1.2 = 6/5
20x - 400 = 18x
2x = 400
x = 200
To solve this problem, we need to use some basic algebra and arithmetic concepts. Let's break it down step by step:
1. Let's first assume that the shopkeeper bought "x" eggs initially.
2. The cost of each egg was rupees 3, so the total cost of "x" eggs would be 3x rupees.
3. Unfortunately, 20 eggs were broken, so the shopkeeper only had "(x - 20)" eggs left to sell.
4. He sold each of these remaining eggs at 4 rupees each. Thus, the total selling price for these eggs would be 4 * (x - 20) rupees.
5. Now, we know that the shopkeeper made a profit of 20%.
Profit = Selling Price - Cost Price
We can calculate the selling price by using the formula:
Selling Price = Cost Price + Profit
In this case, the selling price would be:
Selling Price = 3x + 20% of 3x
Selling Price = 3x + (20/100) * 3x
Selling Price = 3x + (3/5) * x
Selling Price = 3x + (3x/5)
Selling Price = (15x + 3x)/5
Selling Price = (18x)/5
Therefore, the equation becomes:
(18x)/5 = 4 * (x - 20)
6. Now, we can solve this equation to find the value of "x" (the number of eggs the shopkeeper bought).
Multiplying both sides of the equation by 5 to remove the fraction, we get:
18x = 20 * (x - 20)
Expanding the right side:
18x = 20x - 400
Bringing similar terms to one side:
18x - 20x = -400
Simplifying:
-2x = -400
Dividing by -2:
x = -400 / -2
x = 200
Therefore, the shopkeeper bought 200 eggs originally.
Note: We neglected the possibility of fractional eggs in this calculation, assuming that all the numbers (cost price and selling price) are whole numbers.
Let's solve this step-by-step:
Step 1: Find the cost of one egg.
The shopkeeper bought each egg for 3 rupees.
Step 2: Find the selling price of one egg.
The remaining eggs (after deducting the broken ones) were sold at 4 rupees each.
Step 3: Find the profit percentage.
The shopkeeper made a profit of 20%.
Step 4: Calculate the number of eggs bought.
Let's assume the shopkeeper bought x eggs.
Now, let's solve it step-by-step:
Step 1:
The cost of one egg is 3 rupees.
Step 2:
The remaining eggs were sold at 4 rupees each.
Step 3:
The profit percentage is 20%.
Step 4:
Let's assume the shopkeeper bought x eggs.
Now, let's calculate the selling price of one egg (Step 2):
Selling price of one egg = Cost price of one egg + Profit on one egg
= 3 rupees + (20/100) * 3 rupees
= 3 + (0.2 * 3)
= 3 + 0.6
= 3.6 rupees
Since the selling price of one egg is 4 rupees, we can set up an equation:
3.6 rupees * x = 4 rupees * (x - 20)
Now, let's solve the equation to find the value of x:
3.6x = 4(x - 20)
3.6x = 4x - 80
4x - 3.6x = 80
0.4x = 80
x = 80 / 0.4
x = 200
Therefore, the shopkeeper bought 200 eggs.