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# A trader purchases ${\mathbf{70}}$kg of tea at Rs ${\mathbf{15}}$per kg and 30kg of tea at Rs ${\mathbf{18}}.{\mathbf{50}}$ per kg . If the packing charges are ${\mathbf{2}}$ percent, then at what price must he sell the mixture of two gain${\mathbf{15}}\%$?A.Rs.18.82 per kgB.Rs.18 per kgC.Rs.18.50 per kgD.Rs.17.80 per kg

Last updated date: 13th Jun 2024
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Answer
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Hint: Cost price: - The price at which an article is purchase is called its cost price (C.P)
Selling Price: - Price at which an article is sold is called its selling price (SP)
Profit: - If $SP > CP$ the we make a profit
Profit = SP - CP
Loss: - If $CP > SP$ then we make a loss

Complete step by step solution:
Given,
A trade purchase $70$kg of tea at Rs $15$per kg
$1kg\,tea = Rs15$
Cost of $70$ kg of tea at Rs. $15$Per
$Kg = 70 \times 15$
$= 1050\,Rs.$
Now, also given that
$30$ kg of tea at Rs. $18.50$per kg
So, cost of $1$ kg of tea $= 18.50$
Then
Cost of 30kg of tea at 18.50 per kg $= 30 \times \dfrac{{1850}}{{10}}$
$= 555$Rs
Then
The total cost$= 1050\,Rs. + 555\,Rs. = 1605\,Rs.$
Selling price including packing charges or  and gain $15\%$
So, selling price $= \cos t\,price \times \dfrac{{102}}{{100}} \times \dfrac{{115}}{{100}}$
Putting the value of total cost here
$= 1605 \times \dfrac{{102}}{{100}} \times \dfrac{{115}}{{100}}$
$= 1605 \times 1.02 \times 1.15$
$= 1605 \times 1.173$
$S.P = 1882.67$Rs.
Now,
Total weight $= 70 + 30 = 100kg$
Selling price per kg
$= \dfrac{{1882.67}}{{100}}$
$= 18.82$per kg
Hence the answer is $18.82$ per kg.

Note:
1.Profit% and loss % are always calculated on the C.P. and never on the S.P.
2.When C.P. and S.P. are given from an equal number of quantities first find the C.P or S.P. of equal number of quantities and then calculate profit% or loss %.