Question
The salaries of A,B and C are in the ratio 4: 5:6After
one yearbased on their work A's and C's salaries are increased by 5% and 15%, respectively, and B's salary is decreased by 10%. Find the new ratio of their salariesSolution
ATQ, Let's calculate the new ratio of their salaries after the changes. Initially, the ratio of their salaries was 4:5:6. After the changes: A's salary increased by 5%, which means it becomes 105% of the initial salary. B's salary decreased by 10%, which means it becomes 90% of the initial salary. C's salary increased by 15%, which means it becomes 115% of the initial salary. Now, let's calculate the new ratio: Let the initial salaries of A, B, and C be 4x, 5x, and 6x, respectively, where x is a positive constant. After the changes: A's new salary = 4x × 105% = 4.2x B's new salary = 5x × 90% = 4.5x C's new salary = 6x × 115% = 6.9x Now, the new ratio of their salaries: New ratio = (A's new salary) : (B's new salary) : (C's new salary) New ratio = (4.2x) : (4.5x) : (6.9x) Now, we can simplify this ratio by dividing all terms by the greatest common divisor (GCD), which is x: New ratio = (4.2x/x) : (4.5x/x) : (6.9x/x) New ratio = 4.2 : 4.5 : 6.9 To make the ratio more straightforward, we can multiply all terms by 10 to remove decimals: New ratio = (4.2 × 10) : (4.5 × 10) : (6.9 × 10) New ratio = 42 : 45 : 69 So, the new ratio of their salaries after the changes is 42:45:69 or 14:15:23
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