A man spend Rs. 810 in buying trouser at Rs. 70 each and shirt at Rs. 30 each. What will be the ratio of trouser and shirt when the maximum number of trouser is purchased ?

Options

A. A) 1:3
B. B) 2:1
C. C) 3:2
D. D) 2:3

Answer

To solve the problem, we need to determine the maximum number of trousers that can be purchased with Rs. 810, given that each trouser costs Rs. 70 and each shirt costs Rs. 30. We will then find the ratio of trousers to shirts purchased.

### Step-by-Step Solution:

1. **Define Variables**:
Let \( T \) be the number of trousers purchased and \( S \) be the number of shirts purchased.

2. **Set Up the Equation**:
The total cost of trousers and shirts can be expressed as:
\[ 70T + 30S = 810 \]
This equation represents the total expenditure of Rs. 810.

3. **Maximize Trousers**:
To maximize the number of trousers, we should minimize the number of shirts. Therefore, we can set \( S = 0 \) (i.e., purchase no shirts).
\[ 70T + 30(0) = 810 \]
Simplifying this gives:
\[ 70T = 810 \]

4. **Solve for T**:
Now, divide both sides by 70 to find the maximum number of trousers:
\[ T = \frac{810}{70} = 11.57 \]
Since \( T \) must be a whole number, we take the maximum whole number less than or equal to 11.57, which is \( T = 11 \).

5. **Calculate Remaining Money**:
Now, calculate the total cost for 11 trousers:
\[ \text{Cost of trousers} = 11 \times 70 = 770 \]
The remaining money after buying trousers is:
\[ 810 - 770 = 40 \]

6. **Calculate Number of Shirts**:
Now, we can buy shirts with the remaining money. Each shirt costs Rs. 30, so the number of shirts that can be purchased is:
\[ S = \frac{40}{30} = 1.33 \]
Again, since \( S \) must be a whole number, we take \( S = 1 \).

7. **Final Count**:
Thus, the maximum number of trousers purchased is \( T = 11 \) and the number of shirts purchased is \( S = 1 \).

8. **Calculate the Ratio**:
The ratio of trousers to shirts is:
\[ \text{Ratio} = \frac{T}{S} = \frac{11}{1} = 11:1 \]

### Final Answer:
The ratio of trousers to shirts when the maximum number of trousers is purchased is **11:1**.