How many kgs of Basmati rice costing Rs. 42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs. 24 per kg so that he makes a profit of 25% on selling the mixture at Rs. 40/kg?Options :20 kgs12.5 kgs16 kgs200 kgs
Question
How many kgs of Basmati rice costing Rs. 42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs. 24 per kg so that he makes a profit of 25% on selling the mixture at Rs. 40/kg?Options :20 kgs12.5 kgs16 kgs200 kgs
Solution
The problem can be solved using the concept of weighted averages.
Let's denote the amount of Basmati rice (costing Rs. 42/kg) that needs to be mixed with the ordinary rice as 'x' kgs.
The cost price of the mixture per kg will be the weighted average of the cost prices of the Basmati and ordinary rice, which can be calculated as follows:
(42x + 2425) / (x + 25)
According to the problem, the shopkeeper makes a profit of 25% by selling the mixture at Rs. 40/kg. Therefore, the cost price of the mixture per kg should be 75% of the selling price, which is Rs. 30/kg.
Setting the two equations equal to each other, we get:
(42x + 2425) / (x + 25) = 30
Solving this equation for 'x', we get:
42x + 2425 = 30*(x + 25)
42*x + 600 = 30x + 750
12*x = 150
x = 150 / 12
x = 12.5 kgs
Therefore, the shopkeeper should mix 12.5 kgs of Basmati rice with the 25 kgs of ordinary rice.
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