A woman buys spirit at Rs.60 per litre, adds water to it and then sells it at Rs.75 per litre. What is the ratio of the spirit to water if her profit in the deal is 37.5%? radio_button_unchecked 9:1 radio_button_unchecked 10:1 radio_button_unchecked 11:1 radio_button_unchecked 5:1
Question
A woman buys spirit at Rs.60 per litre, adds water to it and then sells it at Rs.75 per litre. What is the ratio of the spirit to water if her profit in the deal is 37.5%?
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radio_button_unchecked 10:1
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Solution
First, let's understand the problem. The woman is buying spirit at Rs.60 per litre and selling it at Rs.75 per litre. Her profit is 37.5%.
The profit percentage is calculated as (Selling Price - Cost Price)/Cost Price * 100.
Given that the profit is 37.5%, we can set up the equation as follows:
37.5 = (75 - 60)/60 * 100
Solving this equation, we find that the cost price of the mixture is Rs.60 per litre.
Now, the woman is adding water to the spirit, which is free of cost. So, the cost price of the spirit remains Rs.60 per litre, and the selling price is Rs.75 per litre.
The profit is therefore Rs.15 per litre (75 - 60), which is 25% of the cost price of the spirit (15/60 * 100).
This means that the ratio of spirit to water in the mixture is 4:1 (since 25% means 1/4). However, this is the ratio of the cost price of the spirit to the cost price of the water.
Since water is free, the entire cost price of the mixture is due to the spirit. Therefore, the ratio of the volume of spirit to the volume of water is also 4:1.
So, the correct answer is:
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