Tea Mixing Ratio Calculation
The problem asks for the ratio in which two types of tea, priced at Rs. 300/kg and Rs. 240/kg, must be mixed to sell the resulting mixture at Rs. 270/kg without any profit or loss. This means the cost price (CP) of the mixture must be equal to the selling price (SP), which is Rs. 270/kg.
Applying the Alligation Rule
The rule of alligation is used to find the ratio of quantities when two ingredients of known prices are mixed to form a mixture of a desired mean price.
Let:
- $P_1$ = Price of the dearer tea = Rs. 300/kg
- $P_2$ = Price of the cheaper tea = Rs. 240/kg
- $P_m$ = Mean Price (Desired selling price) = Rs. 270/kg
The ratio is calculated as:
Ratio = (Price of Dearer Tea - Mean Price) : (Mean Price - Price of Cheaper Tea)
Ratio = ($P_1 - P_m$) : ($P_m - P_2$)
Calculation
Substitute the values:
- Difference 1 = $300 - 270 = 30$
- Difference 2 = $270 - 240 = 30$
The mixing ratio is:
Ratio = $30 : 30$
Simplifying the ratio:
Ratio = $1 : 1$
Conclusion
The merchant should mix the two types of tea in a 1:1 ratio to sell the mixture at Rs. 270/kg without profit or loss.
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Rice worth ₹43/kg and ₹67/kg are mixed with a third variety in the ratio 2 : 1 : 5. If the mixture is worth ₹96/kg, the price (in ₹) of the third variety of rice per kg will be:
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If a + b + c = 0, then the value of (a² + b² + 2ab) is equal to:
