Question No 48.A trader spent a total of Rs.840 to purchase two varieties of sugar. If the selling price of each variety of sugar was Rs.10 per kg more than the cost price, then the profit would be Rs.450. If the cost price of the first variety is Rs.5 less than the second one and the quantities purchased are in the ratio 2 : 1, what is the cost price (in Rs. per kg) of the second variety of sugar?
Question
Question No 48.A trader spent a total of Rs.840 to purchase two varieties of sugar. If the selling price of each variety of sugar was Rs.10 per kg more than the cost price, then the profit would be Rs.450. If the cost price of the first variety is Rs.5 less than the second one and the quantities purchased are in the ratio 2 : 1, what is the cost price (in Rs. per kg) of the second variety of sugar?
Solution
Let's denote the cost price per kg of the first variety of sugar as x, and the cost price per kg of the second variety of sugar as y.
According to the problem, we know that:
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The trader spent a total of Rs.840 to purchase two varieties of sugar. So, the total cost price of the sugar is Rs.840.
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The selling price of each variety of sugar was Rs.10 per kg more than the cost price. So, the total selling price of the sugar is Rs.840 + Rs.450 = Rs.1290.
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The cost price of the first variety is Rs.5 less than the second one. So, x = y - Rs.5.
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The quantities purchased are in the ratio 2 : 1. So, the trader bought twice as much of the first variety of sugar as the second one.
From these four points, we can set up the following equations:
2x + y = Rs.840 (from point 1 and 4) 2(x + Rs.10) + (y + Rs.10) = Rs.1290 (from point 2 and 4) x = y - Rs.5 (from point 3)
Solving these equations, we get:
y = Rs.20 per kg
So, the cost price per kg of the second variety of sugar is Rs.20.
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