Question:
Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio
- 18 : 25
- 19 : 24
- 21 : 25
- 17 : 25
The selling price of the mixture is Rs.40/kg.
Let a be the quantity of tea A in the mixture and b be the quantity of tea B in the mixture.
It has been given that the profit is 10% if the 2 varieties are mixed in the ratio 3:2
Let the cost price of the mixture be x.
It has been given that 1.1x = 40
x = 40/1.1
$\frac{3a+2b}{5} = \frac{40}{1.1}$
$3.3a+2.2b=200$ --------(1)
The profit is 5% if the 2 varieties are mixed in the ratio 2:3.
$\frac{2a+3b}{5} = \frac{40}{1.05}$
$2.1a+3.15b=200$ ------(2)
Equating (1) and (2), we get,
$3.3a+2.2b = 2.1a+3.15b$
$1.2a=0.95b$
$\frac{a}{b} = \frac{0.95}{1.2}$
$\frac{a}{b} = \frac{19}{24}$
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