Question

The salaries of A, B, and C are of ratio 2 : 3 : 5. If the increments of 15%, 10%, and 20% are done to their respective salaries, then find the new ratio of their salaries.

• A. 20 : 33 : 60
• B. 21 : 33 : 60
• C. 22 : 33 : 60
• D. 23 : 33 : 60

Hint:

To find the new ratio after percentage changes, multiply the original amounts by \( 1 + \frac{\text{percentage increment}}{100} \) and simplify the ratio.

Answer 1

The Correct Option is D

Let the original salaries of A, B, and C be \( 2x, 3x, \) and \( 5x \) respectively. 
Step 1: After a 15\% increment for A, the new salary of A is: \[ A' = 2x \times \left(1 + \frac{15}{100}\right) = 2x \times 1.15 = 2.3x \] For B, after a 10\% increment, the new salary of B is: \[ B' = 3x \times \left(1 + \frac{10}{100}\right) = 3x \times 1.10 = 3.3x \] For C, after a 20\% increment, the new salary of C is: \[ C' = 5x \times \left(1 + \frac{20}{100}\right) = 5x \times 1.20 = 6x \] 
Step 2: The new ratio of their salaries is: \[ A' : B' : C' = 2.3x : 3.3x : 6x \] 
Step 3: Simplify the ratio: \[ A' : B' : C' = 23 : 33 : 60 \] Thus, the new ratio of their salaries is \( 23 : 33 : 60 \).