You want to decorate your house with 300 light bulbs of four selected colours. You already have 32 red, 26 green and 9 yellow bulbs. You have no blue bulbs. Each bulb costs Rs 15 and you get 20% discount if you purchase 50 or more bulbs of the same colour and 30% discount when you purchase 70 or more bulbs of one colour. How much would you spend if you decorated your house with an equal number of bulbs of each colour?
A)Rs `2959.50`
B)Rs 2970
C)Rs `2680.50`
D)Rs 2780

Options

A. Rs `2959.50`
B. Rs 2970
C. Rs `2680.50`
D. Rs 2780

Answer

To solve the problem step by step, we need to determine how many bulbs of each color are needed, calculate the total cost, and apply the appropriate discounts.

### Step 1: Determine the total number of bulbs needed for each color
We need a total of 300 bulbs divided equally among 4 colors:
- Total bulbs = 300
- Number of colors = 4
- Bulbs needed per color = 300 / 4 = 75 bulbs

### Step 2: Calculate how many more bulbs are needed for each color
We already have:
- Red bulbs = 32
- Green bulbs = 26
- Yellow bulbs = 9
- Blue bulbs = 0

Now, calculate the number of additional bulbs needed for each color:
- Red: 75 - 32 = 43
- Green: 75 - 26 = 49
- Yellow: 75 - 9 = 66
- Blue: 75 - 0 = 75

### Step 3: Calculate the cost for each color
Each bulb costs Rs 15. We will calculate the cost for each color and apply discounts where applicable.

#### Red Bulbs
- Need: 43
- Cost without discount = 43 * 15 = Rs 645
- No discount applies (less than 50 bulbs).

#### Green Bulbs
- Need: 49
- Cost without discount = 49 * 15 = Rs 735
- No discount applies (less than 50 bulbs).

#### Yellow Bulbs
- Need: 66
- Cost without discount = 66 * 15 = Rs 990
- Discount: 20% (since we are buying more than 50 bulbs).
- Discount amount = 20% of 990 = 0.20 * 990 = Rs 198
- Cost after discount = 990 - 198 = Rs 792.

#### Blue Bulbs
- Need: 75
- Cost without discount = 75 * 15 = Rs 1125
- Discount: 30% (since we are buying more than 70 bulbs).
- Discount amount = 30% of 1125 = 0.30 * 1125 = Rs 337.5
- Cost after discount = 1125 - 337.5 = Rs 787.5.

### Step 4: Calculate the total cost
Now, we add the costs of all the bulbs:
- Total cost = Cost of Red + Cost of Green + Cost of Yellow + Cost of Blue
- Total cost = 645 + 735 + 792 + 787.5
- Total cost = 2959.5

### Final Answer
The total amount spent on decorating the house with the bulbs is Rs 2959.50.