Question : Two types of tea, costing Rs.180 per kg and Rs. 280 per kg, should be mixed in a ratio so that the mixture obtained, sold at Rs. 320 per kg to earn a profit of 20%, is:
Option 1: 3 : 13
Option 2: 1 : 13
Option 3: 4 : 13
Option 4: 2 : 13
Correct Answer: 2 : 13
Solution :
Given: The selling price of the mixture is Rs. 320 and the profit is 20%.
So, the cost price of the mixture is $= 320 × \frac{100}{100+20}=\frac{800}{3}$
Let the ratio of the two types of tea in the mixture be $= x:y$
According to the question,
$180x + 280y = \frac{800}{3}(x+y)$
⇒ $540x + 840y = 800(x+y)$
⇒ $800x-540x = 840y-800y$
⇒ $260x = 40y$
$\therefore x:y = 4 : 26 = 2 : 13$
Hence, the correct answer is 2 : 13.
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