Shanti bought lemons at 7 foe Rs.6
and sold them at 6 for Rs.7. (1).find her profit percentage (2).how many lemons would she have to sell to earn a profit of Rs.65?
unit cost price = 6/7 or appr .8571
unit selling price = 7/6 or appr 1.1667
profit per unit = 7/6 - 6/7 = 13/42 = appr .3096
or appr 30.96%
13/42 x = 65
x = 65(42/13) = 209.95
or appr 210
210 lemons must be sold
Not understood
To find the profit percentage, we need to calculate the cost price (CP) and the selling price (SP) of the lemons.
Given information:
- Shanti bought lemons at 7 for Rs.6, so the cost price of each lemon is 6/7 Rs.
- Shanti sold lemons at 6 for Rs.7, so the selling price of each lemon is 7/6 Rs.
(1) Profit Percentage:
Profit = Selling Price - Cost Price
Profit = (7/6) - (6/7)
To simplify this calculation, we can find the LCM (Least Common Multiple) of the denominators (6 and 7), which is 42.
Profit = (7/6 * 42/42) - (6/7 * 42/42)
Profit = (294/252) - (252/252)
Profit = 42/252
To convert the profit into a percentage, we multiply it by 100.
Profit Percentage = (42/252) * 100
Profit Percentage = 16.67%
Therefore, Shanti's profit percentage is 16.67%.
(2) To find out how many lemons Shanti needs to sell to earn a profit of Rs.65, we need to calculate the number of lemons (N) with the given information.
Profit = Selling Price - Cost Price
Profit = Rs.65
Given information:
- Shanti bought lemons at 7 for Rs.6, so the cost price of each lemon is 6/7 Rs.
We can calculate the selling price of each lemon by dividing the profit by the number of lemons sold.
Selling Price per lemon = (Cost Price per lemon + Profit per lemon) = (6/7 + 65/N) Rs.
Given that Shanti sold lemons at 6 for Rs.7, we can set up the equation:
(6/7 + 65/N) = 7/6
To solve this equation, we can cross-multiply.
(6/7 + 65/N) = 7/6
(6/7)(6) + 65/N = (7/6)(7)
36/7 + 65/N = 49/6
To simplify this equation, we multiply both sides by 42N to eliminate the fractions.
(36/7)(42N) + (65/N)(42N) = (49/6)(42N)
36(6N) + 65(7) = 49(7N)
216N + 455 = 343N
Rearranging the equation, we get:
343N - 216N = 455
127N = 455
N = 455/127
Calculating this, we find:
N ≈ 3.5827
Therefore, Shanti would have to sell approximately 3.5827 lemons to earn a profit of Rs.65. Since we cannot sell a portion of a lemon, she would need to sell at least 4 lemons to earn a profit of Rs.65.
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