The cost of a pair of trousers was 55% the cost of a shirt. If Shubham intended to buy a pair of trousers and shirt both, then how much money must he have, if the shirt costs Rs. 31.50 more than the pair of trousers?

Options

A. Rs. 38.50
B. Rs. 70
C. Rs. 108.50
D. Rs. 120.55

Answer

To solve the problem, we need to set up equations based on the information given in the question. Let's break it down step by step.

### Step 1: Define Variables
Let the cost of the shirt be \( S \) and the cost of the trousers be \( T \).

### Step 2: Set Up the Relationships
According to the problem:
1. The cost of the trousers is 55% of the cost of the shirt:
\[ T = 0.55S \]

2. The shirt costs Rs. 31.50 more than the trousers:
\[ S = T + 31.50 \]

### Step 3: Substitute the Value of T
Now, we can substitute the value of \( T \) from the first equation into the second equation:
\[ S = 0.55S + 31.50 \]

### Step 4: Solve for S
To isolate \( S \), we can rearrange the equation:
\[ S - 0.55S = 31.50 \]
\[ 0.45S = 31.50 \]
Now, divide both sides by 0.45:
\[ S = \frac{31.50}{0.45} \]
Calculating this gives:
\[ S = 70 \]

### Step 5: Find the Cost of Trousers
Now that we have the cost of the shirt, we can find the cost of the trousers using the first equation:
\[ T = 0.55S = 0.55 \times 70 = 38.50 \]

### Step 6: Total Cost
Finally, to find out how much money Shubham needs to buy both the shirt and trousers, we add the two costs together:
\[ \text{Total Cost} = S + T = 70 + 38.50 = 108.50 \]

### Final Answer
Shubham must have Rs. 108.50.

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