In an electric appliances shop there were some fans and coolers containing 3 blades and 4 blades each respectively along with a motor each. The cost of a fan is Rs. 1200 and that of cooler is Rs. 3000. One day due to short circuit the shop caught the fire. After extinguishing the fire, shopkeeper has estimated that 90 sets of motor bodies and 320 blades were burned and then nothing was left useful in his shop. What is the loos incurred from the coolers alone?

Options

A. Rs. 1,50,000
B. Rs. 12,000
C. Rs. 4800
D. can't be determined

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define Variables
Let:
- \( X \) = number of fans
- \( Y \) = number of coolers

### Step 2: Set Up Equations
From the problem, we know:
1. Each fan has 1 motor and each cooler has 1 motor. The total number of motors is 90.
\[ X + Y = 90 \quad \text{(Equation 1)} \]

2. Each fan has 3 blades and each cooler has 4 blades. The total number of blades is 320.
\[ 3X + 4Y = 320 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
We will solve these two equations simultaneously. First, we can express \( X \) from Equation 1:
\[ X = 90 - Y \]

Now, substitute \( X \) in Equation 2:
\[ 3(90 - Y) + 4Y = 320 \]
Expanding this gives:
\[ 270 - 3Y + 4Y = 320 \]
Combining like terms:
\[ 270 + Y = 320 \]
Now, isolate \( Y \):
\[ Y = 320 - 270 = 50 \]

### Step 4: Find the Number of Fans
Now substitute \( Y \) back into Equation 1 to find \( X \):
\[ X + 50 = 90 \]
Thus,
\[ X = 90 - 50 = 40 \]

### Step 5: Calculate Loss from Coolers
Now we know:
- Number of coolers \( Y = 50 \)
- Cost of one cooler = Rs. 3000

Total loss from coolers:
\[ \text{Loss} = \text{Number of Coolers} \times \text{Cost of One Cooler} = 50 \times 3000 = 150000 \]

### Final Answer
The loss incurred from the coolers alone is Rs. 150,000.

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