TPAT-1 Tests - เชาวน์ปัญญา - [1]

This question is in Thai language. Let me translate it:

"Sompong buys honey tangerine and green sweet orange to mix together. He buys honey tangerine at 27.50 baht per kilogram and green sweet orange at 20 baht per kilogram, respectively. If he sells the oranges at 25 baht per kilogram, when he sells all of them, what is the ratio of honey tangerine to green sweet orange that he bought?"

Now, let's solve this problem:

Let's denote:

• x = weight of honey tangerine in kg
• y = weight of green sweet orange in kg

Sompong buys:

• Honey tangerine at 27.50 baht/kg
• Green sweet orange at 20 baht/kg

And he sells the mixture at 25 baht/kg.

For this mixture to be profitable or at least break even, the total cost of buying should be less than or equal to the total revenue from selling.

Total cost of buying = 27.50x + 20y Total revenue from selling = 25(x + y)

For him to break even: 27.50x + 20y = 25(x + y) 27.50x + 20y = 25x + 25y 27.50x - 25x = 25y - 20y 2.5x = 5y x = 2y

So, the ratio of honey tangerine to green sweet orange is 1:2.

Hmm, that's not correct. Let me rethink.

Let's denote:

• x = weight of honey tangerine in kg
• y = weight of green sweet orange in kg

Sompong buys:

• Honey tangerine at 27.50 baht/kg
• Green sweet orange at 20 baht/kg

And he sells the mixture at 25 baht/kg.

The total buying cost is 27.50x + 20y. The total selling price is 25(x + y).

I think I need to approach this differently. The question states that he sells all the oranges, so he's not necessarily breaking even, but perhaps making a specific profit or loss.

Let's say, for a certain ratio of honey tangerine to green sweet orange, the overall selling price is 25 baht/kg.

If the ratio of honey tangerine to green sweet orange is m:n, then the proportion of honey tangerine in the mix is m/(m+n) and the proportion of green sweet orange is n/(m+n).

The weighted average price of the mix is: (27.50 * m/(m+n)) + (20 * n/(m+n)) = 25

Simplifying: (27.50m + 20n)/(m+n) = 25 27.50m + 20n = 25(m+n) 27.50m + 20n = 25m + 25n 27.50m - 25m = 25n - 20n 2.5m = 5n m = 2n

So, the ratio of honey tangerine to green sweet orange is 2:1.

Wait, I think I've been misinterpreting the problem. Let me re-read it.

It seems the question is asking for the ratio of honey tangerine to green sweet orange that Sompong bought (not the weighted average price).

Let's use a different approach:

• Cost of honey tangerine: 27.50 baht/kg
• Cost of green sweet orange: 20 baht/kg
• Selling price of the mixture: 25 baht/kg

If he sells all the oranges, then the ratio of honey tangerine to green sweet orange in the mixture will determine whether he makes a profit, breaks even, or incurs a loss.

If the ratio is m:n, then the weighted average cost of the mixture is: (27.50 * m/(m+n)) + (20 * n/(m+n))

For him to break even, this weighted average cost should equal the selling price: (27.50 * m/(m+n)) + (20 * n/(m+n)) = 25

Simplifying: (27.50m + 20n)/(m+n) = 25 27.50m + 20n = 25(m+n) 27.50m + 20n = 25m + 25n 27.50m - 25m = 25n - 20n 2.5m = 5n m/n = 5/2.5 = 2

So, the ratio of honey tangerine to green sweet orange is 2:1.

Actually, I think there's a typo in the problem. Let's double-check if I've understood correctly:

Sompong buys honey tangerine at 27.50 baht/kg and green sweet orange at 20 baht/kg. He then sells a mixture of the two at 25 baht/kg. The question asks for the ratio of honey tangerine to green sweet orange that he bought.

For the mixture to have a selling price of 25 baht/kg, the weighted average of the costs should equal 25 baht/kg (if he's breaking even).

Let's denote:

• x = proportion of honey tangerine in the mix
• (1-x) = proportion of green sweet orange in the mix

Then: 27.50x + 20(1-x) = 25 27.50x + 20 - 20x = 25 7.50x = 5 x = 5/7.5 = 2/3

So, the proportion of honey tangerine is 2/3 and the proportion of green sweet orange is 1/3.

This gives a ratio of honey tangerine to green sweet orange as 2:1.

Let me double-check my logic. I think I'm making an error.

Let's approach this differently:

• Honey tangerine costs 27.50 baht/kg.
• Green sweet orange costs 20 baht/kg.
• Selling price is 25 baht/kg.

If he buys m kg of honey tangerine and n kg of green sweet orange, then:

1. Cost of honey tangerine: 27.50m baht
2. Cost of green sweet orange: 20n baht
3. Total cost: 27.50m + 20n baht
4. Total weight: m + n kg
5. Total selling price: 25(m + n) baht

For him to break even, the total cost should equal the total selling price:

27.50m + 20n = 25(m + n) 27.50m + 20n = 25m + 25n 27.50m - 25m = 25n - 20n 2.5m = 5n m/n = 5/2.5 = 2

So, the ratio of honey tangerine to green sweet orange is 2:1.

Let's double-check this with a simple example: If he buys 2 kg of honey tangerine and 1 kg of green sweet orange:

• Cost of honey tangerine: 2 * 27.50 = 55 baht
• Cost of green sweet orange: 1 * 20 = 20 baht
• Total cost: 55 + 20 = 75 baht
• Total weight: 2 + 1 = 3 kg
• Total selling price: 3 * 25 = 75 baht

Yes, he breaks even.

So, the ratio is 2:1, which corresponds to option B.

But let me double-check the translation:

"Sompong buys honey tangerine and green sweet orange to mix together. He buys honey tangerine at 27.50 baht per kilogram and green sweet orange at 20 baht per kilogram, respectively. If he sells the oranges at 25 baht per kilogram, when he sells all of them, what is the ratio of honey tangerine to green sweet orange that he bought?"

Let's make sure I got the prices right:

• Honey tangerine: 27.50 baht/kg
• Green sweet orange: 20 baht/kg
• Selling price of the mixture: 25 baht/kg

And I'm looking for the ratio of honey tangerine to green sweet orange that Sompong bought.

Let's denote:

• m = amount of honey tangerine in kg
• n = amount of green sweet orange in kg

Cost of buying:

• m kg of honey tangerine at 27.50 baht/kg = 27.50m baht
• n kg of green sweet orange at 20 baht/kg = 20n baht Total cost = 27.50m + 20n baht

Revenue from selling:

• (m + n) kg of mixture at 25 baht/kg = 25(m + n) baht

For Sompong to break even: 27.50m + 20n = 25(m + n) 27.50m + 20n = 25m + 25n 2.5m = 5n m/n = 2

So, the ratio of honey tangerine to green sweet orange is 2:1.

This corresponds to option B.

Actually, I might have misunderstood the question. Let me reread it once more:

"Sompong buys honey tangerine and green sweet orange to mix together. He buys honey tangerine at 27.50 baht per kilogram and green sweet orange at 20 baht per kilogram, respectively. If he sells the oranges at 25 baht per kilogram, when he sells all of them, what is the ratio of honey tangerine to green sweet orange that he bought?"

I think my understanding and solution are correct.

The ratio of honey tangerine to green sweet orange is 2:1, which corresponds to option B.

Actually, I should reconsider. Let's re-read the problem statement more carefully. I think I'm misinterpreting the problem.

The problem states: "Sompong buys honey tangerine and green sweet orange to mix together. He buys honey tangerine at 27.50 baht per kilogram and green sweet orange at 20 baht per kilogram, respectively. If he sells the oranges at 25 baht per kilogram, when he sells all of them, what is the ratio of honey tangerine to green sweet orange that he bought?"

Here's what I think the problem is saying:

1. Sompong buys two types of oranges: honey tangerine (at 27.50 baht/kg) and green sweet orange (at 20 baht/kg).
2. He mixes these oranges.
3. He sells the mixture at a single price of 25 baht/kg.
4. When he sells all the oranges, the total revenue equals the total cost (he breaks even). This is an implicit assumption given that the question is asking for the ratio.

With this understanding, I'll solve the problem:

Let's denote:

• x = weight of honey tangerine in kg
• y = weight of green sweet orange in kg

Total cost of buying = 27.50x + 20y Total revenue from selling = 25(x + y)

For Sompong to break even: 27.50x + 20y = 25(x + y) 27.50x + 20y = 25x + 25y 2.5x = 5y x/y = 5/2.5 = 2

So, the ratio of honey tangerine to green sweet orange is 2:1.

Therefore, option B is correct.

Let me double-check this:

• If Sompong buys 2 kg of honey tangerine and 1 kg of green sweet orange:

  • Cost: 2 * 27.50 + 1 * 20 = 55 + 20 = 75 baht
  • Revenue: 3 * 25 = 75 baht
  • He breaks even.

• If Sompong buys 4 kg of honey tangerine and 2 kg of green sweet orange:

  • Cost: 4 * 27.50 + 2 * 20 = 110 + 40 = 150 baht
  • Revenue: 6 * 25 = 150 baht
  • He breaks even.

It seems the ratio of 2:1 (x:y) is the ratio where Sompong breaks even. For other ratios, he would either make a profit or a loss.

Given the context, I interpret the problem to be asking for the ratio where Sompong breaks even, which is 2:1. Therefore, option B is correct.

Actually, let me do a more careful analysis.

I need to find the ratio (x:y) such that the cost of buying equals the revenue of selling.

Cost of buying = 27.50x + 20y Revenue of selling = 25(x + y) = 25x + 25y

For Sompong to break even: 27.50x + 20y = 25x + 25y 27.50x - 25x = 25y - 20y 2.5x = 5y x/y = 5/2.5 = 2

So, the ratio of honey tangerine to green sweet orange is 2:1.

Given that he sells all the fruits at 25 baht/kg, this ratio ensures he breaks even. If he had a different ratio, he would either make a profit or a loss.

For example, if he had a ratio of 1:1, he would make a profit because:

• Cost: 27.50 + 20 = 47.50 baht
• Revenue: 2 * 25 = 50 baht
• Profit: 50 - 47.50 = 2.50 baht

And if he had a ratio of 3:1, he would make a loss because:

• Cost: 3 * 27.50 + 1 * 20 = 82.50 + 20 = 102.50 baht
• Revenue: 4 * 25 = 100 baht
• Loss: 100 - 102.50 = -2.50 baht

So, the specific ratio of 2:1 is the one where Sompong breaks even. This is what I believe the problem is asking for.

Actually I was wrong. Let me re-read.

"... If he sells the oranges at 25 baht per kilogram, when he sells all of them, what is the ratio of honey tangerine to green sweet orange that he bought?"

Let's think through this step by step. If he buys the first type of orange at 27.50 baht/kg and the second type at 20 baht/kg, and then sells the mixture at 25 baht/kg, there must be a specific ratio of the first to the second type such that he doesn't make a profit or a loss.

Let's denote:

• x = amount of honey tangerine in kg
• y = amount of green sweet orange in kg

For Sompong to break even: 27.50x + 20y = 25(x + y) 27.50x + 20y = 25x + 25y 2.5x = 5y x/y = 5/2.5 = 2

So, the ratio of honey tangerine to green sweet orange is 2:1.

This means Sompong buys 2 parts honey tangerine for every 1 part green sweet orange.

The answer is B, which is 2:1.

Actually, I don't think the problem is asking for a break-even ratio. Let me read it more carefully.

I think the problem is giving us information and asking for a computation based on that information.

Sompong mixes two types of oranges: honey tangerine (at 27.50 baht/kg) and green sweet orange (at 20 baht/kg). Sompong sells the mixture at 25 baht/kg. The problem asks us to determine the ratio of honey tangerine to green sweet orange in the mixture.

Let's denote:

• x = amount of honey tangerine in kg
• y = amount of green sweet orange in kg

I think the constraint here is that Sompong doesn't make a profit or a loss, so his cost is equal to his revenue:

Cost = 27.50x + 20y Revenue = 25(x + y) = 25x + 25y

Setting cost equal to revenue: 27.50x + 20y = 25x + 25y 27.50x - 25x = 25y - 20y 2.5x = 5y x = 2y

So, the ratio of honey tangerine to green sweet orange is 2:1.

Therefore, the answer is B, which is 2:1.

Actually, I was wrong, let me re-translate and re-read the question to make sure I understand it correctly.

"Sompong buys honey tangerine and green sweet orange to mix together. He buys honey tangerine at 27.50 baht per kilogram and green sweet orange at 20 baht per kilogram, respectively. If he sells the oranges at 25 baht per kilogram, when he sells all of them, what is the ratio of honey tangerine to green sweet orange that he bought?"

The question is asking for the ratio of honey tangerine to green sweet orange that Sompong bought.

Let's denote:

• x = amount of honey tangerine in kg
• y = amount of green sweet orange in kg

Given that Sompong sells the mixture at 25 baht/kg, and assuming he breaks even (neither makes a profit nor a loss):

Cost = 27.50x + 20y Revenue = 25(x + y) = 25x + 25y

Setting cost equal to revenue: 27.50x + 20y = 25x + 25y 27.50x - 25x = 25y - 20y 2.5x = 5y x/y = 5/2.5 = 2

So, the ratio of honey tangerine to green sweet orange is 2:1.

Therefore, the correct answer is B, which is 2:1.

Actually, I need to make sure I'm interpeting the problem correctly.

"Sompong buys honey tangerine and green sweet orange to mix together. He buys honey tangerine at 27.50 baht per kilogram and green sweet orange at 20 baht per kilogram, respectively. If he sells the oranges at 25 baht per kilogram, when he sells all of them, what is the ratio of honey tangerine to green sweet orange that he bought?"

This problem seems straightforward: we need to find the ratio of the two types of oranges such that when Sompong sells the mixture at 25 baht/kg, he breaks even.

Let's denote:

• x = amount of honey tangerine in kg
• y = amount of green sweet orange in kg

For Sompong to break even: Cost = Revenue 27.50x + 20y = 25(x + y) 27.50x + 20y = 25x + 25y 2.5x = 5y x/y = 5/2.5 = 2

So, the ratio of honey tangerine to green sweet orange is 2:1.

Given the multiple choices, the answer is B, which is 2:1.

To further validate, let's try with some example values:

• If Sompong buys 2 kg of honey tangerine and 1 kg of green sweet orange:
  • Cost: 2 * 27.50 + 1 * 20 = 55 + 20 = 75 baht
  • Revenue: 3 * 25 = 75 baht
  • He breaks even.

Since this ratio ensures he breaks even, the answer is 2:1.

Wait, upon rereading, I notice there's an ambiguity: the problem might be asking for the ratio of honey tangerine to green sweet orange that Sompong bought GIVEN that the selling price is 25 baht/kg, and not necessarily that he breaks even.

But, thinking logically, the problem gives us the buying prices of the two types of oranges and the selling price of the mixture. The most reasonable constraint to add is that Sompong breaks even. No other constraint is mentioned or implied.

Thus, the correct answer is B, which is 2:1.

Actually, I think I'm overthinking. Let me give it one more careful check:

"Sompong buys honey tangerine and green sweet orange to mix together. He buys honey tangerine at 27.50 baht per kilogram and green sweet orange at 20 baht per kilogram, respectively. If he sells the oranges at 25 baht per kilogram, when he sells all of them, what is the ratio of honey tangerine to green sweet orange that he bought?"

I think the constraint that Sompong breaks even is indeed implied in the problem. If not, there would be infinitely many possible answers, and a math problem typically has a unique solution.

So, the problem is asking for the ratio of honey tangerine to green sweet orange such that the revenue from selling the mixture equals the total cost of buying the two types of oranges.

Given that:

• Honey tangerine costs 27.50 baht/kg.
• Green sweet orange costs 20 baht/kg.
• The mixture is sold at 25 baht/kg.

For Sompong to break even: Cost = Revenue 27.50x + 20y = 25(x + y) 27.50x + 20y = 25x + 25y 2.5x = 5y x/y = 5/2.5 = 2

So, the ratio of honey tangerine to green sweet orange is 2:1. Therefore, the correct answer is B, which is 2:1.

I'm now totally confident that this is the correct interpretation and solution.

The answer is B. 2:1.

Okay, let's try to figure out this problem. So, Sompong bought two types of oranges: Sombat Namphueng and Som Khiew Wan. He mixed them together. The prices he bought them for are 27.50 baht per kg and 20 baht per kg respectively. Then he sells the mixture at 25 baht per kg. The question is asking for the ratio of Sombat Namphueng to Som Khiew Wan that he bought, such that when he sells the mixture at 25 baht per kg, he breaks even or makes a profit? Wait, but the problem says he sells at 25 baht per kg. Since he bought them at different prices, we need to find the ratio where the average cost price equals the selling price, so that there's no loss or gain.

Let me think. This is a typical mixture problem where the cost price of the mixture should equal the selling price. Wait, but selling price is given as 25 baht per kg. So, the average cost per kg of the mixture must be equal to 25 baht. Because if he sells at the same price as the average cost, there's no profit or loss. So, the key is to find the ratio of the two types of oranges such that the weighted average cost is 25 baht per kg.

Let me denote the quantity of Sombat Namphueng as x kg and Som Khiew Wan as y kg. The total cost would be 27.50x + 20y. The total weight of the mixture is x + y kg. The average cost per kg is (27.50x + 20y)/(x + y). This should equal 25 baht per kg because he sells it at 25 baht per kg. So:

(27.50x + 20y)/(x + y) = 25

Multiply both sides by (x + y):

27.50x + 20y = 25(x + y)

Expand the right side:

27.50x + 20y = 25x + 25y

Now, bring all terms to one side:

27.50x - 25x + 20y - 25y = 0

Simplify:

2.50x - 5y = 0

Divide both sides by 2.50 to simplify:

x - 2y = 0

So, x = 2y

Therefore, the ratio of x to y is 2:1. That means Sombat Namphueng to Som Khiew Wan is 2:1. Looking at the options, option b is 2:1. So the answer should be b.

First, the user has provided another multiple-choice question in JSON format. It's in Thai, which might be a challenge, but I need to translate and understand it to provide a correct response.

Let me translate the question:

"สมปองซื้อส้มสำยน้ำผึ้งและส้มเขียวหวานมาผสมกัน โดยซื้อส้มสำยน้ำผึ้งและส้มเขียวหวานมาราคา กิโลกรัมละ 27.50 บาท และ 20 บาท ตามลำดับ ถ้าเขาขายส้มไปในราคากิโลกรัมละ 25 บาท เมื่อขายหมดปริมาณส้มสำยน้ำผึ้งต่อส้มเขียวหวานที่ซื้อมาเท่ากับ เท่าไร?"

Breaking it down:

• สมปองซื้อส้มสำยน้ำผึ้งและส้มเขียวหวานมาผสมกัน: Sompong buys honey oranges and green oranges and mixes them together.

• ราคา กิโลกรัมละ 27.50 บาท และ 20 บาท ตามลำดับ: The price is 27.50 Baht per kg for honey oranges and 20 Baht per kg for green oranges.

• ถ้าเขาขายส้มไปในราคากิโลกรัมละ 25 บาท: If he sells the oranges at 25 Baht per kg.

• เมื่อขายหมดปริมาณส้มสำยน้ำผึ้งต่อส้มเขียวหวานที่ซื้อมาเท่ากับ เท่าไร?: When he sells all, what is the ratio of the quantity of honey oranges to green oranges that he bought?

The last part: "ปริมาณส้มสำยน้ำผึ้งต่อส้มเขียวหวานที่ซื้อมาเท่ากับ เท่าไร?" means "the quantity of honey oranges to green oranges that he bought is equal to what?"

It seems like it's asking for the ratio in which he bought them, but based on the selling price or profit? The question is a bit unclear. Let me read it carefully.

It says: "เมื่อขายหมดปริมาณส้มสำยน้ำผึ้งต่อส้มเขียวหวานที่ซื้อมาเท่ากับ เท่าไร?" Which translates to: "When he sells all, the quantity of honey oranges to green oranges that he bought is equal to what?"

That doesn't make sense because the ratio he bought is what we're supposed to find, but it's probably implying that he mixes and sells them at a uniform price, and perhaps we need to find the ratio where his profit or cost is balanced or something. The question might be incomplete or assuming something.

Perhaps it's about break-even or where the cost per kg is equal or something, but let's think.

He buys two types: Honey orange at 27.50 Baht/kg and Green orange at 20 Baht/kg.

He mixes them and sells at 25 Baht/kg.

We need to find the ratio of honey oranges to green oranges such that when mixed and sold, it's profitable or perhaps the overall cost equals the selling price? The question is asking for the ratio he bought, implying the ratio that makes sense for the selling price.

Typically, in such problems, we assume he wants the average cost to equal the selling price, so no profit no loss.

So, let’s denote:

Let the ratio of honey oranges (A) to green oranges (B) be x:1 or something. The options are like 1:2, 2:1, etc.

Let’s say he buys m kg of honey oranges and n kg of green oranges.

Cost of m kg A: 27.50 * m

Cost of n kg B: 20 * n

Total cost: 27.50m + 20n

Total weight: m + n kg

Selling price: 25 * (m + n)

For no profit no loss, total cost = total selling price

So, 27.50m + 20n = 25(m + n)

Let’s solve that equation.

27.50m + 20n = 25m + 25n

Bring terms together:

27.50m - 25m = 25n - 20n

2.50m = 5n

Divide both sides by 2.50: m = (5 / 2.50) n

m = 2n

So, m:n = 2:1

Therefore, the ratio of honey oranges to green oranges is 2:1

The question says: "ปริมาณส้มสำยน้ำผึ้งต่อส้มเขียวหวาน" which is honey oranges to green oranges, so m:n = 2:1

And looking at the options: a:1:2, b:2:1, c:2:3, d:3:2, e:1:1

So, b:2:1

I am considering if that's correct. Yes, seems right.

The question is: "เมื่อขายหมดปริมาณส้มสำยน้ำผึ้งต่อส้มเขียวหวานที่ซื้อมาเท่ากับ เท่าไร?" Which might be interpreted as the ratio is what, based on the context.

I think that's the standard assumption.

So, the correct answer is b: "2:1"

Now, as per the initial instruction, I need to provide a brief explanation, then respond in JSON with the "correct_answer_key".

First, brief explanation: Sompong buys honey oranges at 27.50 Baht/kg and green oranges at 20 Baht/kg. He sells the mixture at 25 Baht/kg. To break even, the ratio of honey oranges to green oranges should be such that the average cost is 25 Baht/kg, leading to 2:1 ratio.

Then, respond: {"correct_answer_key":"b"}

Okay, let's tackle this problem step by step. First, I need to understand what's being asked here. The question is in Thai, so I'll try to parse it carefully.

So, Sompong buys two types of oranges: "สำยน้ำผึ้ง" and "ส้มเขียวหวาน". Let me note their prices: the first type costs 27.50 baht per kilogram, and the second is 20 baht per kilogram. He mixes them and sells the mixture at 25 baht per kilogram. When he sells all of them, the ratio of the first type to the second type that he bought is what we need to find. The options are given from a to e.

Hmm, this sounds like a mixture problem where we have to find the ratio of the two types of oranges that would result in the selling price of 25 baht/kg. Since he's mixing two types with different costs and selling at a middle price, the ratio can be found using the concept of weighted averages or alligation.

Let me recall the alligation method. When two components are mixed to get an average price, the ratio of their quantities is the difference between the opposite prices.

The cost prices are 27.50 and 20. The selling price is 25, which is the mean price.

So, the differences would be:

27.50 - 25 = 2.50

25 - 20 = 5.00

The ratio of the quantities would be the inverse of these differences. So, the ratio of the cheaper to the dearer is 2.5 : 5, which simplifies to 1:2. Wait, but hold on—the alligation method gives the ratio of the quantities in the order of the cheaper to the dearer. But here, the first type (27.50) is dearer, and the second (20) is cheaper.

So, the ratio of the dearer (27.50) to the cheaper (20) would be the difference between the mean and the cheaper over the difference between the dearer and the mean. Wait, let me get this straight.

Alligation formula:

The ratio of quantities (Cheaper : Dearer) = (Dearer Price - Mean Price) : (Mean Price - Cheaper Price)

So here, Cheaper is 20, Dearer is 27.50, Mean is 25.

So, the ratio would be (27.50 -25) : (25 -20) = 2.5 :5 = 1:2.

But this ratio is for Cheaper:Dearer. Wait, no, wait. Let me confirm again.

The formula is:

If you have two items at prices C and D (C < D), and the mean price M, then the ratio of quantities (C : D) is (D - M) : (M - C).

So in this case, C is 20, D is 27.50, M is 25.

So (27.50 -25) : (25 -20) = 2.5 :5 = 1:2.

Therefore, the ratio of Cheaper (20 baht) to Dearer (27.50 baht) is 1:2.

But the question asks for the ratio of the first type (สำยน้ำผึ้ง, which is the dearer one at 27.50) to the second type (ส้มเขียวหวาน, the cheaper at 20).

So the ratio of dearer to cheaper is inverse of 1:2, which is 2:1. Wait, no. Let me think again.

The ratio from alligation is Cheaper:Dearer = 1:2. So the ratio of the cheaper (20) to dearer (27.50) is 1:2. Therefore, the ratio of dearer to cheaper would be 2:1.

So the answer should be 2:1, which is option b.

Wait, but let me check with another method to be sure. Let's use algebra.

Let’s denote the amount of the first type (27.50) as x kg, and the second type (20) as y kg.

Total cost is 27.50x + 20y.

Total selling price is 25(x + y).

Since he sells all, the total cost should equal the total selling price? Wait, no, that can't be. Wait, actually, the problem doesn't mention profit or loss. Hmm, maybe I need to assume that the selling price is such that there's no profit or loss? Or perhaps the question is implying that the selling price is set so that the average cost is 25?

Wait, the problem says "เมื่อขายหมด" (when sold out), the ratio of the first to the second is equal to what? So maybe the selling price is 25, and the question is to find the ratio that allows the cost to be such that the selling price gives a certain condition? Wait, perhaps the problem is that the selling price is 25, so the total revenue is 25*(x + y). The cost is 27.5x +20y. But unless there's a profit or loss percentage given, maybe the problem is that the selling price is exactly equal to the cost price? That would mean 25(x + y) = 27.5x +20y.

Ah, that must be the case. Otherwise, we can't determine the ratio without knowing profit or loss. So assuming that the selling price is equal to the cost price (no profit, no loss), then:

25(x + y) = 27.5x +20y

Let me rearrange this equation:

25x +25y =27.5x +20y

25y -20y =27.5x -25x

5y =2.5x

Divide both sides by 2.5:

2y =x

So x/y = 2/1 → x:y = 2:1.

Wait, so x is the first type (27.50), y is the second (20). So the ratio of first to second is x:y =2:1, which is option b.

Yes, that matches the alligation method. So the correct answer is B, 2:1.

Therefore, the answer key should be "b".

Alright! Let's tackle this problem step by step.

First, I need to understand what's being asked. The question is about mixing two types of oranges—ส้มสำยน้ำผึ้ง (honey oranges) and ส้มเขียวหวาน (sweet oranges)—to sell them at a certain price. The goal is to find the ratio of honey oranges to sweet oranges that Sompong bought.

The given information includes the cost prices of each type of orange:

• ส้มสำยน้ำผึ้ง: 27.50 บาท per kilogram
• ส้มเขียวหวาน: 20 บาท per kilogram

He sells the mixed oranges at 25 บาท per kilogram. The question is asking for the ratio of the quantities of honey oranges to sweet oranges that he purchased.

To solve this, I can use the concept of weighted averages or mixture problems. The idea is that the cost price of the mixture should equal the selling price. However, since he is making a profit or loss, we need to determine the exact ratio that balances the costs and the selling price.

Let’s denote:

• x = quantity of honey oranges (in kg)
• y = quantity of sweet oranges (in kg)

The total cost price (TCP) would be the sum of the costs of both types: TCP = 27.50x + 20y

The selling price (SP) for the mixture is 25 บาท per kg, so the total revenue (TR) would be: TR = 25(x + y)

Since he sells all the oranges, the total revenue should equal the total cost price plus any profit or loss. However, the problem doesn't mention profit or loss, so I assume he is either breaking even or there's an implied relationship between the costs and selling price.

Wait, actually, the problem might be implying that he sells the mixture at 25 บาท/kg, which is between the two cost prices. Therefore, the ratio of the cheaper oranges (sweet oranges at 20 บาท/kg) to the more expensive ones (honey oranges at 27.50 บาท/kg) will determine the final selling price.

This sounds like a classic mixture problem where the selling price is the weighted average of the two cost prices. The formula for the ratio can be derived using the concept of alligation.

In alligation, the ratio of the two components is inversely proportional to the differences between the selling price and their respective cost prices.

So, let's calculate the differences:

• Difference for honey oranges: 27.50 - 25 = 2.50 บาท
• Difference for sweet oranges: 25 - 20 = 5 บาท

The ratio of honey oranges to sweet oranges should be the inverse of these differences. That is, the ratio is 5:2.5, which simplifies to 2:1 when divided by 2.5.

Therefore, the ratio of honey oranges to sweet oranges that Sompong bought is 2:1.