Question

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

• A. 38000
• B. 24000
• C. 32000
• D. 34000

Answer 1

Answer:

A. 38000

• Representing Salaries: When salaries or quantities are given in a ratio, like 2:3, it is best to represent them using a common multiple. Let Ravi's initial salary be 2x and Sumit's initial salary be 3x, where 'x' is a common factor. This is a fundamental step in solving ratio-based problems.

• Incorporating the Increment: The problem states that the salary of each person is increased by Rs. 4000. Therefore, their new salaries become:

  • Ravi's new salary = (2x + 4000)

  • Sumit's new salary = (3x + 4000)

• Setting up the Equation: The new ratio of their salaries is given as 40:57. We can form a proportion based on these new salaries:

  
  (2x + 4000) / (3x + 4000) = 40 / 57

  This proportion forms the core equation to solve for 'x'.

• Solving for 'x' using Cross-Multiplication:

  1. Cross-multiply the terms: 57 * (2x + 4000) = 40 * (3x + 4000)

  2. Distribute the numbers: 114x + 228000 = 120x + 160000

  3. Isolate 'x' terms on one side and constant terms on the other: 228000 - 160000 = 120x - 114x

  4. Simplify the equation: 68000 = 6x

  5. Solve for 'x': x = 68000 / 6 = 34000 / 3

• Calculating Original (Present) Salaries: Now that 'x' is found, substitute it back into the initial salary expressions:

  • Ravi's original salary = 2x = 2 * (34000/3) = Rs. 68000/3

  • Sumit's original (present) salary = 3x = 3 * (34000/3) = Rs. 34000

• Calculating New Salaries: Determine their salaries after the increment:

  • Ravi's new salary = (68000/3) + 4000 = (68000 + 12000)/3 = Rs. 80000/3

  • Sumit's new salary = 34000 + 4000 = Rs. 38000