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Re: HOT Competition: Rice of two different varieties A and B are mixed tog
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26 Aug 2020, 00:05
The answer is A.
This question took 2 hours to solve..
I was having a hard time to get the meaning of “a loss of 15%”.
I think that this question is a wake up call for me. Because I’ve always solved the profit/loss question using the formula «\(x*(1± \frac{r}{100})\)» without proper understanding of the formula, this 2-hours-of-digging-a-hole situation happened ?.
So this is what I learnt from this question.
“I bought a lemon at $10 and want a profit of 50% from reselling the lemon. At what price I should sell the lemon?”
: She should sell it at $15. Because the profit she want is 50% from what she spent on the lemon. 50% of $10 is $5, using the formula \(10*\frac{50}{100}\)
Thus, To calculate selling price, we use\(10\)(the cost)\(+\)\((10*\frac{50}{100})\)(the profit), which is exactly same as \(10*(1+\frac{50}{100})\)
“I bought a lemon at $10 and incurred a loss of 40% because of miscalculation of selling price. Guess how much I sold the lemon”
: She sold the lemon at $6. Because she had \(10*\frac{40}{100}=$4\) loss. So she earned $0 and left with $-4 account.
To calculate selling price, \(10\)(the cost)\(+\)\((10*\frac{-40}{100})\)(the loss), which is exactly same as \(10*(1-\frac{40}{100})\).
Back to the question,
Rice of two different varieties A and B are mixed together in the ratio of 4:7. Upon selling the mixture at the price of $17 per kg, the seller incurred a loss of 15%. Cost price of B is $22 per kg. What is the cost price per kg of A?
-> since we want to know cost price per kg of A, let’s say that the total kg of the mixture is 1kg, and the cost price per kg of A is \(x\)
In the mixture, there is \(\frac{4}{11}kg\) of A, \(\frac{7}{11}kg\) of B.
Cost price of each is \($\frac{4x}{11}\) and \($\frac{7*22}{11}=\frac{154}{11}\). Thus, total cost price is \(\frac{4x+154}{11}\).
Sale price is \($17\).
$ loss amount is 15% of the cost; \(\frac{4x+154}{11}*\frac{15}{100}=\frac{12x+462}{220}\).
Therefore, \(cost-loss=sale price, \frac{4x+154}{11}-\frac{12x+462}{220}=17\).
When you solve the equation above, you’ll get \(x=15\)
Thus, the cost price per kg of A is $15.
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