Study the following information carefully and answer the questions given below:
Amy has decided to start a new company named ‘Amy Travels’. She wants to buy some furniture - table, chair, air-conditioners. She also wants to buy a few desktops, which will include monitor, CPU, keyboard and mouse, and the cost- of each table is 13.5 times the cost of a mouse and the cost of a chair is `3/5` of the cost of a table. The cost of an air-conditioner is 5 times the cost of a chair. The cost of a monitor is `20%` more than the cost of a chair. A CPU costs ₹1500 more than a table and the keyboard costs 4 times a mouse. The cost of a mouse is ₹1000.
What is the ratio of the cost of a CPU to the cost of a mouse and keyboard together?

Options

A. `3:2`
B. `4:1`
C. `3:1`
D. `5:1`

Answer

To solve the problem step by step, we will first determine the costs of each item based on the information provided.

### Step 1: Find the cost of the mouse
The cost of a mouse is given as:
- **Cost of a mouse = ₹1000**

### Step 2: Find the cost of the table
The cost of a table is 13.5 times the cost of a mouse:
- **Cost of a table = 13.5 × Cost of a mouse**
- **Cost of a table = 13.5 × ₹1000 = ₹13500**

### Step 3: Find the cost of the chair
The cost of a chair is \( \frac{3}{5} \) of the cost of a table:
- **Cost of a chair = \( \frac{3}{5} \) × Cost of a table**
- **Cost of a chair = \( \frac{3}{5} \) × ₹13500 = ₹8100**

### Step 4: Find the cost of the air-conditioner
The cost of an air-conditioner is 5 times the cost of a chair:
- **Cost of an air-conditioner = 5 × Cost of a chair**
- **Cost of an air-conditioner = 5 × ₹8100 = ₹40500**

### Step 5: Find the cost of the monitor
The cost of a monitor is 20% more than the cost of a chair:
- **Cost of a monitor = Cost of a chair + 20% of Cost of a chair**
- **Cost of a monitor = ₹8100 + (0.2 × ₹8100)**
- **Cost of a monitor = ₹8100 + ₹1620 = ₹9720**

### Step 6: Find the cost of the CPU
The cost of a CPU is ₹1500 more than the cost of a table:
- **Cost of CPU = Cost of a table + ₹1500**
- **Cost of CPU = ₹13500 + ₹1500 = ₹15000**

### Step 7: Find the cost of the keyboard
The cost of a keyboard is 4 times the cost of a mouse:
- **Cost of keyboard = 4 × Cost of a mouse**
- **Cost of keyboard = 4 × ₹1000 = ₹4000**

### Step 8: Calculate the total cost of the mouse and keyboard together
- **Total cost of mouse and keyboard = Cost of mouse + Cost of keyboard**
- **Total cost of mouse and keyboard = ₹1000 + ₹4000 = ₹5000**

### Step 9: Find the ratio of the cost of the CPU to the cost of the mouse and keyboard together
- **Ratio = Cost of CPU : Total cost of mouse and keyboard**
- **Ratio = ₹15000 : ₹5000**

To simplify the ratio, divide both sides by ₹5000:
- **Ratio = 15000 ÷ 5000 : 5000 ÷ 5000**
- **Ratio = 3 : 1**

### Final Answer:
The ratio of the cost of a CPU to the cost of a mouse and keyboard together is **3:1**.

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