A screw driver and a hammer currently have the same price. If the price of a screw driver rises by` 5%` and the price of hammer goes up by`3%`, then how much more will it cost to buy 3 screw drivers and 3 hammers?

Options

A. 20
B. 22
C. 24
D. 25

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Define the initial price
Let the initial price of both the screwdriver and the hammer be \( P \). For simplicity, we can assume \( P = 100 \) (this will make calculations easier).

### Step 2: Calculate the new price of the screwdriver
The price of the screwdriver increases by 5%. Therefore, the new price of the screwdriver can be calculated as:
\[ \text{New Price of Screwdriver} = P + (5\% \text{ of } P) = P + 0.05P = 1.05P \]
Substituting \( P = 100 \):
\[ \text{New Price of Screwdriver} = 1.05 \times 100 = 105 \]

### Step 3: Calculate the new price of the hammer
The price of the hammer increases by 3%. Therefore, the new price of the hammer can be calculated as:
\[ \text{New Price of Hammer} = P + (3\% \text{ of } P) = P + 0.03P = 1.03P \]
Substituting \( P = 100 \):
\[ \text{New Price of Hammer} = 1.03 \times 100 = 103 \]

### Step 4: Calculate the total cost of 3 screwdrivers and 3 hammers at the new prices
Now, we need to calculate the total cost for 3 screwdrivers and 3 hammers at their new prices:
\[ \text{Total Cost} = 3 \times (\text{New Price of Screwdriver}) + 3 \times (\text{New Price of Hammer}) \]
Substituting the new prices:
\[ \text{Total Cost} = 3 \times 105 + 3 \times 103 = 315 + 309 = 624 \]

### Step 5: Calculate the total cost of 3 screwdrivers and 3 hammers at the old prices
Now, we calculate the total cost for 3 screwdrivers and 3 hammers at their old prices:
\[ \text{Total Old Cost} = 3 \times P + 3 \times P = 3 \times 100 + 3 \times 100 = 300 + 300 = 600 \]

### Step 6: Calculate the difference in cost
Now, we find the difference in cost:
\[ \text{Difference} = \text{Total Cost} - \text{Total Old Cost} = 624 - 600 = 24 \]

### Step 7: Conclusion
Thus, it will cost an additional \( 24 \) to buy 3 screwdrivers and 3 hammers after the price increases.