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Given Cost price of Milk = Rs 6/litre Calculation We want to sell the mixture at cost price and still gain 25%. So, we simply add 25% of water 25% of water means = 25/100 = 1/4 so, the ratio of water and milk to gain 25% profit = 1 : 4 ∴ The required answer is 1 : 4. India’s #1 Learning Platform Start Complete Exam Preparation
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Mock Tests & Quizzes Trusted by 3.4 Crore+ Students Answer Hint: This is a mixture alligation problem. To solve this first we will obtain the gain amount and cost price of mixture. And then by using a mixture and alligation rule we will obtain the ratio or water and milk. Complete step-by-step answer: Let the cost price of 1 liter of milk = Rs.1According to the question, cost price of milk is equal to the selling price of mixture (mixture of milk and water)Hence the selling price of 1 liter of mixture = Rs.1Gain = 16%Hence the cost price of mixture = \[\dfrac{{100}}{{100 + gain\% }} \times SP\] ( Here SP means selling price )\[ = \dfrac{{100}}{{100 + 16}} \times 1\]$ = \dfrac{{100}}{{116}} = \dfrac{{25}}{{29}}$rs.By the rule of mixture and alligation,Cost price of 1 liter of water, c = 0Cost price of 1 liter of milk, d = 1Mean price, m = cost price of mixture =$\dfrac{{25}}{{29}}$Hence, d-m = $1 - \dfrac{{25}}{{29}} = \dfrac{{29 - 25}}{{29}} = \dfrac{4}{{29}}$And m-c = $\dfrac{{25}}{{29}} - 0 = \dfrac{{25}}{{29}}$Therefore the ratio of water and milk in the mixture is,d-m : m-c$ = \dfrac{4}{{29}}:\dfrac{{25}}{{29}}$As the denominator of both the terms are equal, hence the ratio is 4:25.Therefore, in a 4:25 ratio water must be mixed with milk to gain 16% on selling the mixture at cost price.So, the correct answer is “Option B”. Note: You might get confused because the selling price of the mixture is equal to the cost price of the milk as it is trickily mentioned in the question. We can also solve this by using alternative methods.Alternative method- Let the amount of water mixed is x literCP of milk = SP of mixture = 1(let)Actual CP of mixture is 100/116By adding water we get profit 16/116Therefore for every 100 liter of milk, 16 liter of water is added.Hence the ratio of water and milk in the mixture is 16/100 = 4/25 = 4:25 |
In what ratio should a vendor mix water with milk to gain 12 00 to 30% on selling the mixture at cost price?
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