In what ratio a man must mix pulses at Rs. 11.10 per kg with Rs. 15.20 per kg pulse so as to make a mixture worth Rs. 13.20 per kg ?

Options

A. `4 : 3`
B. `16 : 27`
C. `4 : 7`
D. `20 : 21`

Answer

To solve the problem of mixing two types of pulses at different prices to achieve a desired price for the mixture, we can use the concept of alligation. Here’s a step-by-step solution:

### Step 1: Identify the prices of the pulses
Let:
- Price of the first pulse (P1) = Rs. 11.10 per kg
- Price of the second pulse (P2) = Rs. 15.20 per kg
- Price of the mixture (Pm) = Rs. 13.20 per kg

### Step 2: Calculate the differences
We need to find the differences between the prices of the pulses and the price of the mixture.

- Difference between P2 and Pm:
\[ D1 = P2 - Pm = 15.20 - 13.20 = 2.00 \]

- Difference between Pm and P1:
\[ D2 = Pm - P1 = 13.20 - 11.10 = 2.10 \]

### Step 3: Set up the ratio
According to the alligation method, the ratio of the quantities of the two pulses is inversely proportional to the differences calculated above.

Thus, the ratio of the first pulse to the second pulse is given by:
\[ \text{Ratio} = \frac{D2}{D1} = \frac{2.10}{2.00} \]

### Step 4: Simplify the ratio
To simplify the ratio:
\[ \frac{2.10}{2.00} = \frac{21}{20} \]

### Step 5: Write the final answer
The ratio in which the man must mix the two pulses is:
\[ \text{Ratio} = 21 : 20 \]