The total cost of 8 buckets and 5 mugs is Rs. 92 and the total cost of 5 buckets and 8 mugs is Rs. 77. Find the cost of 2 mugs and 3 buckets.

Options

A. Rs. 35
B. Rs. 70
C. Rs. 30
D. Rs. 38

Answer

To solve the problem step by step, we need to set up equations based on the information given.

### Step 1: Define Variables
Let:
- \( x \) = cost of 1 bucket
- \( y \) = cost of 1 mug

### Step 2: Set Up Equations
From the problem, we have two equations based on the total costs:
1. For 8 buckets and 5 mugs:
\( 8x + 5y = 92 \) (Equation 1)

2. For 5 buckets and 8 mugs:
\( 5x + 8y = 77 \) (Equation 2)

### Step 3: Solve the Equations
We will solve these equations simultaneously.

First, let's multiply Equation 1 by 5 and Equation 2 by 8 to eliminate \( x \):

- From Equation 1:
\( 5(8x + 5y) = 5(92) \)
\( 40x + 25y = 460 \) (Equation 3)

- From Equation 2:
\( 8(5x + 8y) = 8(77) \)
\( 40x + 64y = 616 \) (Equation 4)

### Step 4: Subtract the Equations
Now, we will subtract Equation 3 from Equation 4 to eliminate \( x \):

\[ (40x + 64y) - (40x + 25y) = 616 - 460 \]

This simplifies to:

\[ 64y - 25y = 156 \]
\[ 39y = 156 \]

### Step 5: Solve for \( y \)
Now, divide both sides by 39:

\[ y = \frac{156}{39} = 4 \]

### Step 6: Substitute \( y \) Back to Find \( x \)
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):

\[ 8x + 5(4) = 92 \]
\[ 8x + 20 = 92 \]
\[ 8x = 92 - 20 \]
\[ 8x = 72 \]
\[ x = \frac{72}{8} = 9 \]

### Step 7: Find the Cost of 2 Mugs and 3 Buckets
Now we need to find the cost of 2 mugs and 3 buckets:

- Cost of 3 buckets:
\( 3x = 3 \times 9 = 27 \)

- Cost of 2 mugs:
\( 2y = 2 \times 4 = 8 \)

### Step 8: Total Cost
Now, add the costs together:

\[ \text{Total Cost} = \text{Cost of 3 buckets} + \text{Cost of 2 mugs} = 27 + 8 = 35 \]

### Final Answer
The cost of 2 mugs and 3 buckets is **Rs. 35**.

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