Out of the total bags, `30%` of bags are green coloured. `30%` of remaining bags are red coloured. `40%` of remaining bags are yellow coloured. The remaining 1176 bags are blue coloured. How many total bags are there?

Options

A. 3000
B. 4000
C. 5000
D. 6000

Answer

To solve the problem step by step, let's denote the total number of bags as \( x \).

### Step 1: Calculate the number of green bags
30% of the total bags are green. Therefore, the number of green bags is:
\[ \text{Green bags} = 0.30 \times x = \frac{30}{100} \times x = \frac{3}{10}x \]

### Step 2: Calculate the remaining bags after green bags
The remaining bags after removing the green bags are:
\[ \text{Remaining bags} = x - \text{Green bags} = x - \frac{3}{10}x = \frac{7}{10}x \]

### Step 3: Calculate the number of red bags
30% of the remaining bags are red. Therefore, the number of red bags is:
\[ \text{Red bags} = 0.30 \times \left(\frac{7}{10}x\right) = \frac{3}{10} \times \frac{7}{10}x = \frac{21}{100}x \]

### Step 4: Calculate the remaining bags after red bags
The remaining bags after removing the red bags are:
\[ \text{Remaining bags} = \frac{7}{10}x - \frac{21}{100}x \]
To perform this subtraction, we need a common denominator (100):
\[ \frac{7}{10}x = \frac{70}{100}x \]
Thus,
\[ \text{Remaining bags} = \frac{70}{100}x - \frac{21}{100}x = \frac{49}{100}x \]

### Step 5: Calculate the number of yellow bags
40% of the remaining bags are yellow. Therefore, the number of yellow bags is:
\[ \text{Yellow bags} = 0.40 \times \left(\frac{49}{100}x\right) = \frac{40}{100} \times \frac{49}{100}x = \frac{1960}{10000}x = \frac{49}{250}x \]

### Step 6: Calculate the remaining bags after yellow bags
The remaining bags after removing the yellow bags are:
\[ \text{Remaining bags} = \frac{49}{100}x - \frac{49}{250}x \]
To perform this subtraction, we need a common denominator (250):
\[ \frac{49}{100}x = \frac{122.5}{250}x \]
Thus,
\[ \text{Remaining bags} = \frac{122.5}{250}x - \frac{49}{250}x = \frac{73.5}{250}x \]

### Step 7: Set the remaining bags equal to the number of blue bags
According to the problem, the remaining bags are 1176, which are blue:
\[ \frac{73.5}{250}x = 1176 \]

### Step 8: Solve for \( x \)
To find \( x \), multiply both sides by 250:
\[ 73.5x = 1176 \times 250 \]
Calculating the right side:
\[ 1176 \times 250 = 294000 \]
Now, divide both sides by 73.5:
\[ x = \frac{294000}{73.5} \]
Calculating this gives:
\[ x = 4000 \]

### Conclusion
The total number of bags is \( \boxed{4000} \).

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