How many kgs of rice of variety-1 costing Rs.42/kg should a shopkeeper mix with 25 kgs of rice of variety-2 costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
Question
How many kgs of rice of variety-1 costing Rs.42/kg should a shopkeeper mix with 25 kgs of rice of variety-2 costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg?
Solution
Let's denote the amount of rice of variety-1 that the shopkeeper should mix as X kg.
The cost price of X kg of variety-1 rice is Rs.42X. The cost price of 25 kg of variety-2 rice is Rs.24*25 = Rs.600.
So, the total cost price of the mixture is Rs.42X + Rs.600.
The shopkeeper sells the mixture at Rs.40/kg and makes a profit of 25%. This means the cost price of the mixture is 75% of the selling price.
Therefore, we can set up the following equation:
75% of Rs.40*(X+25) = Rs.42X + Rs.600.
Solving this equation will give us the value of X, the amount of variety-1 rice the shopkeeper should mix.
0.75 * 40 * (X+25) = 42X + 600 30X + 750 = 42X + 600 12X = 150 X = 150 / 12 X = 12.5 kg
So, the shopkeeper should mix 12.5 kg of rice of variety-1 with 25 kg of rice of variety-2.
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