Salaries of Akash, Bablu and Chintu are in the ratio of 2 : 3 : 5. If their salaries were increased by 15%, 10% and 20% respectively, then what will be the new ratio of their salaries?

Options

A. `3 : 3 : 10 `
B. `23 : 33 : 60`
C. `20 : 22 : 40 `
D. None of these

Answer

To solve the problem, we need to follow these steps:

### Step 1: Define the Salaries
Let the salaries of Akash, Bablu, and Chintu be represented as:
- Akash's salary = 2k
- Bablu's salary = 3k
- Chintu's salary = 5k

### Step 2: Calculate the Increased Salaries
Next, we will calculate the new salaries after the respective increases:
- Akash's salary increase by 15%:
\[ \text{New Salary of Akash} = 2k + 0.15 \times 2k = 2k \times \frac{115}{100} = \frac{230k}{100} = \frac{23k}{10} \]

- Bablu's salary increase by 10%:
\[ \text{New Salary of Bablu} = 3k + 0.10 \times 3k = 3k \times \frac{110}{100} = \frac{330k}{100} = \frac{33k}{10} \]

- Chintu's salary increase by 20%:
\[ \text{New Salary of Chintu} = 5k + 0.20 \times 5k = 5k \times \frac{120}{100} = \frac{600k}{100} = \frac{60k}{10} \]

### Step 3: Write the New Salaries
Now we have the new salaries:
- New Salary of Akash = \(\frac{23k}{10}\)
- New Salary of Bablu = \(\frac{33k}{10}\)
- New Salary of Chintu = \(\frac{60k}{10}\)

### Step 4: Form the New Ratio
To find the new ratio of their salaries, we will write it as:
\[ \text{New Ratio} = \frac{\frac{23k}{10}}{\frac{33k}{10}} : \frac{\frac{33k}{10}}{\frac{60k}{10}} : \frac{\frac{60k}{10}}{\frac{60k}{10}} \]
This simplifies to:
\[ \text{New Ratio} = 23 : 33 : 60 \]

### Step 5: Simplify the Ratio
To simplify the ratio \(23 : 33 : 60\), we check for common factors. Since there are no common factors among 23, 33, and 60, the ratio remains:
\[ \text{Final New Ratio} = 23 : 33 : 60 \]

### Conclusion
The new ratio of their salaries after the respective increases is \(23 : 33 : 60\).

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