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In what ratio must water be mixed with milk to gain 16 2/3 % on selling the mixture at cost price?
- a)6:1
- b)1:6
- c)1:4
- d)4:1
Correct answer is option 'B'. Can you explain this answer?
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In what ratio must water be mixed with milk to gain 16 2/3 % on sellin...
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In what ratio must water be mixed with milk to gain 16 2/3 % on sellin...
Given:
- Gain on selling mixture at cost price = 16 2/3 % = 1/6
To find: Ratio of water to milk
Let's assume that we mix 1 unit of milk with some units of water. So, the total mixture will be 1 + x units.
We want to find the ratio of water to milk, so let's assume that we mix m units of water with 1 unit of milk. So, the total mixture will be m + 1 units.
Calculation:
- According to the question, gain on selling the mixture at cost price = 1/6
- Selling price of 1 unit of mixture = Cost price of 1 unit of mixture + Gain
- Let's assume that cost price of 1 unit of mixture = Rs. 1
- Selling price of 1 unit of mixture = Rs. 1 + Rs. 1/6 = Rs. 7/6
- Selling price of 1 unit of mixture = (m + 1) / (m + 1 + 1) * Selling price of 1 unit of water + 1 / (m + 1 + 1) * Selling price of 1 unit of milk (As the total mixture is m + 1 units and it contains m units of water and 1 unit of milk)
- Selling price of 1 unit of water = Cost price of 1 unit of water + Gain on 1 unit of water = Rs. 1 + Rs. 1/6 * Rs. 1 = Rs. 7/6
- Selling price of 1 unit of milk = Cost price of 1 unit of milk + Gain on 1 unit of milk = Rs. 1 + Rs. 1/6 * Rs. 1 = Rs. 7/6
- Substituting the values, we get: Rs. 7/6 = (m / (m + 2)) * Rs. 7/6 + (1 / (m + 2)) * Rs. 7/6
- Simplifying, we get: m = 5
- So, the required ratio of water to milk = 5:1 = 1:5
Therefore, the correct answer is option B) 1:6.
- Gain on selling mixture at cost price = 16 2/3 % = 1/6
To find: Ratio of water to milk
Let's assume that we mix 1 unit of milk with some units of water. So, the total mixture will be 1 + x units.
We want to find the ratio of water to milk, so let's assume that we mix m units of water with 1 unit of milk. So, the total mixture will be m + 1 units.
Calculation:
- According to the question, gain on selling the mixture at cost price = 1/6
- Selling price of 1 unit of mixture = Cost price of 1 unit of mixture + Gain
- Let's assume that cost price of 1 unit of mixture = Rs. 1
- Selling price of 1 unit of mixture = Rs. 1 + Rs. 1/6 = Rs. 7/6
- Selling price of 1 unit of mixture = (m + 1) / (m + 1 + 1) * Selling price of 1 unit of water + 1 / (m + 1 + 1) * Selling price of 1 unit of milk (As the total mixture is m + 1 units and it contains m units of water and 1 unit of milk)
- Selling price of 1 unit of water = Cost price of 1 unit of water + Gain on 1 unit of water = Rs. 1 + Rs. 1/6 * Rs. 1 = Rs. 7/6
- Selling price of 1 unit of milk = Cost price of 1 unit of milk + Gain on 1 unit of milk = Rs. 1 + Rs. 1/6 * Rs. 1 = Rs. 7/6
- Substituting the values, we get: Rs. 7/6 = (m / (m + 2)) * Rs. 7/6 + (1 / (m + 2)) * Rs. 7/6
- Simplifying, we get: m = 5
- So, the required ratio of water to milk = 5:1 = 1:5
Therefore, the correct answer is option B) 1:6.
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In what ratio must water be mixed with milk to gain 16 2/3 % on sellin...
If he add 25 percentage of water the profit would have been 33%
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In what ratio must water be mixed with milk to gain 16 2/3 % on selling the mixture at cost price?a)6:1b)1:6c)1:4d)4:1Correct answer is option 'B'. Can you explain this answer?
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