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The price of a box and a pen is Rs.60. The box was sold at a 40% profit and the pen at a loss of 10%. If the Shop keeper gains Rs.4 in the whole transaction, then how much is the cost price of Box?
- a)Rs.10
- b)Rs.30
- c)Rs.20
- d)Rs.40
- e)None of the Above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The price of a box and a pen is Rs.60. The box was sold at a 40% profi...
Answer – C. Rs.20 Explanation : 40x/100 – 10(60-x)/100 = 4 40x + 10x = 400 + 600 x = 20
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The price of a box and a pen is Rs.60. The box was sold at a 40% profi...
Given:
- The price of a box and a pen is Rs.60.
- The box was sold at a 40% profit.
- The pen was sold at a loss of 10%.
- The shopkeeper gains Rs.4 in the whole transaction.
To find:
The cost price of the box.
Solution:
Let's assume the cost price of the box is 'x' and the cost price of the pen is 'y'.
1. Cost price equation:
From the given information, we can write the equation:
x + y = 60 ...(1)
2. Selling price equation:
The box was sold at a 40% profit, so the selling price of the box is:
Selling price of box = Cost price of box + 40% of cost price of box
Selling price of box = x + 0.4x = 1.4x
The pen was sold at a loss of 10%, so the selling price of the pen is:
Selling price of pen = Cost price of pen - 10% of cost price of pen
Selling price of pen = y - 0.1y = 0.9y
The total selling price of the box and the pen is Rs.60, so we can write the equation:
1.4x + 0.9y = 60 ...(2)
3. Profit equation:
The shopkeeper gains Rs.4 in the whole transaction, so we can write the equation:
Selling price - Cost price = Profit
(1.4x + 0.9y) - (x + y) = 4
0.4x - 0.1y = 4 ...(3)
To solve the equations (1), (2), and (3), we can use the method of substitution or elimination.
Using the substitution method, we can solve equations (1) and (3) simultaneously to find the values of x and y.
From equation (1), we can express y in terms of x:
y = 60 - x
Substituting this value of y in equation (3):
0.4x - 0.1(60 - x) = 4
0.4x - 6 + 0.1x = 4
0.5x = 10
x = 10/0.5
x = 20
Therefore, the cost price of the box is Rs.20. Hence, option C is the correct answer.
- The price of a box and a pen is Rs.60.
- The box was sold at a 40% profit.
- The pen was sold at a loss of 10%.
- The shopkeeper gains Rs.4 in the whole transaction.
To find:
The cost price of the box.
Solution:
Let's assume the cost price of the box is 'x' and the cost price of the pen is 'y'.
1. Cost price equation:
From the given information, we can write the equation:
x + y = 60 ...(1)
2. Selling price equation:
The box was sold at a 40% profit, so the selling price of the box is:
Selling price of box = Cost price of box + 40% of cost price of box
Selling price of box = x + 0.4x = 1.4x
The pen was sold at a loss of 10%, so the selling price of the pen is:
Selling price of pen = Cost price of pen - 10% of cost price of pen
Selling price of pen = y - 0.1y = 0.9y
The total selling price of the box and the pen is Rs.60, so we can write the equation:
1.4x + 0.9y = 60 ...(2)
3. Profit equation:
The shopkeeper gains Rs.4 in the whole transaction, so we can write the equation:
Selling price - Cost price = Profit
(1.4x + 0.9y) - (x + y) = 4
0.4x - 0.1y = 4 ...(3)
To solve the equations (1), (2), and (3), we can use the method of substitution or elimination.
Using the substitution method, we can solve equations (1) and (3) simultaneously to find the values of x and y.
From equation (1), we can express y in terms of x:
y = 60 - x
Substituting this value of y in equation (3):
0.4x - 0.1(60 - x) = 4
0.4x - 6 + 0.1x = 4
0.5x = 10
x = 10/0.5
x = 20
Therefore, the cost price of the box is Rs.20. Hence, option C is the correct answer.
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The price of a box and a pen is Rs.60. The box was sold at a 40% profit and the pen at a loss of 10%. If the Shop keeper gains Rs.4 in the whole transaction, then how much is the cost price of Box?a)Rs.10b)Rs.30c)Rs.20d)Rs.40e)None of the AboveCorrect answer is option 'C'. Can you explain this answer?
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