Question : The salaries of X, Y, and Z are in the ratio 8 : 5 : 12. If their salaries are increased by 10%, 20%, and 30% respectively, then what will be the ratio of their increased salaries?
Option 1: 22 : 15 : 39
Option 2: 25 : 48 : 59
Option 3: 24 : 47 : 58
Option 4: 11 : 25 : 36
Correct Answer: 22 : 15 : 39
Solution :
Let the original salaries be 8$x$, 5$x$ and 12$x$.
After the increment,
⇒ X's new salary $=8x + \frac{10}{100}×8x = 8x + 0.1 × 8x = 8.8x$
⇒ Y' new salary $=5x + \frac{20}{100} ×5x = 5x + 0.2 × 5x = 6x$
⇒ Z' new salary $=12x + \frac{30}{100} ×5x = 12x + 0.3 × 5x = 15.6x$
So, the ratio of X, Y, and Z's salaries
$=8.8x:6x:15.6x = \frac{8.8x}{6x} : \frac{6x}{6x} : \frac{15.6x}{6x} = \frac{22}{15} : 1 : \frac{26}{15} = 22 : 15 : 39$
Hence, the correct answer is 22 : 15 : 39.
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