Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by ₹4000, the new ratio becomes 40:57. What is Sumit's salary?

Let Ravi's original salary be \( 2x \) and Sumit's original salary be \( 3x \), where \( x \) is a common multiplier since their salaries are in the ratio \( 2:3 \).

After an increase of ₹4000 to each salary, the new salaries become:
- Ravi's new salary = \( 2x + 4000 \)
- Sumit's new salary = \( 3x + 4000 \)

We are given that the new ratio of their salaries is \( 40:57 \). Therefore, we can set up the following equation:

\[
\frac{2x + 4000}{3x + 4000} = \frac{40}{57}
\]

Now, cross-multiply to eliminate the fractions:

\[
57(2x + 4000) = 40(3x + 4000)
\]

Expanding both sides:

\[
57 \times 2x + 57 \times 4000 = 40 \times 3x + 40 \times 4000
\]

\[
114x + 228000 = 120x + 160000
\]

Now, move the terms involving \( x \) to one side and constants to the other:

\[
114x - 120x = 160000 - 228000
\]

\[
-6x = -68000
\]

Solve for \( x \):

\[
x = \frac{68000}{6} = 11333.33
\]

Now, Sumit's original salary is \( 3x \):

\[
3x = 3 \times 11333.33 = 34000
\]

Thus, Sumit's original salary is ₹34,000.

### Would you like any further details or clarifications?

### Related Questions:
1. What is Ravi's original salary based on the same ratio?
2. How much is Sumit's salary after the increase of ₹4000?
3. What is the total increase in the combined salary of Ravi and Sumit?
4. If the ratio had been \( 3:4 \) instead of \( 2:3 \), how would the result change?
5. How do ratios affect the relationships between quantities in different situations?

### Tip: Always cross-check ratios by solving step-by-step equations to ensure accuracy when dealing with salary or similar ratio problems.

Learn how to solve the salary problem where Ravi and Sumit's salaries are in a 2:3 ratio. After a ₹4000 increase, the ratio changes to 40:57. This solution explains step-by-step how to calculate Sumit's salary, covering key concepts like ratios and linear equations. Suitable for students in Grades 8-10.

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