The ratio of the quantities of sugar, in which sugar costing 20 per kg. and 15 per kg, should be mixed so that there will be neither loss nor gain on selling the mixed sugar at the rate of 16 per kg, is

Options

A. `2:1`
B. `1:2`
C. `4:1`
D. `1:4`

Answer

To solve the problem of finding the ratio in which sugar costing ₹20 per kg and ₹15 per kg should be mixed so that there is neither loss nor gain when sold at ₹16 per kg, we can follow these steps:

### Step 1: Identify the Cost Prices
We have two types of sugar:
- Sugar A (costing ₹20 per kg)
- Sugar B (costing ₹15 per kg)

### Step 2: Determine the Selling Price
The selling price of the mixture is given as ₹16 per kg.

### Step 3: Set Up the Alligation Formula
To find the ratio of the quantities of the two types of sugar, we can use the alligation method. The formula for alligation is:

\[ \text{Ratio} = \frac{(C_1 - S)}{(S - C_2)} \]

Where:
- \(C_1\) = Cost price of the dearer sugar (₹20)
- \(C_2\) = Cost price of the cheaper sugar (₹15)
- \(S\) = Selling price of the mixture (₹16)

### Step 4: Calculate the Differences
Now, we calculate the differences:
- Difference for the dearer sugar: \(C_1 - S = 20 - 16 = 4\)
- Difference for the cheaper sugar: \(S - C_2 = 16 - 15 = 1\)

### Step 5: Form the Ratio
Now we can form the ratio using the differences calculated:
\[ \text{Ratio} = \frac{4}{1} \]

### Step 6: Simplify the Ratio
The ratio of the quantities of sugar A to sugar B is:
\[ 4:1 \]

### Final Answer
Thus, the ratio in which sugar costing ₹20 per kg and ₹15 per kg should be mixed is **4:1**.

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