The salaries of Karthik, Arun and Akhil are in the ratio 4 : 5 : 6 respectively. Their salaries are then increased by 50 percent, 60 percent and 50 percent respectively. What will be the new ratio of the salaries of Akhil, Arun and Karthik (in that order)?

Introduction / Context:
This question tests ratio manipulation and percentage increase applied to each term of a ratio. The initial ratio of salaries is given, then different percentage increases are applied to each person. Finally, the ratio is asked in a different order than originally stated, so careful reading is important. Such problems model real life scenarios where different employees receive different raise percentages.

Given Data / Assumptions:

• Initial salary ratio: Karthik : Arun : Akhil = 4 : 5 : 6.
• Karthik gets a 50 percent increase.
• Arun gets a 60 percent increase.
• Akhil gets a 50 percent increase.
• We must find the new ratio in the order Akhil : Arun : Karthik.

Concept / Approach:
To handle this, we convert each original salary ratio term into an algebraic value, apply the relevant percentage increase, and obtain new terms. Since ratios can be scaled freely, we do not need actual currency amounts. After calculating the increased values, we arrange them according to the desired order and simplify the ratio if necessary. Percentage increase by p percent is implemented by multiplying the original quantity by (1 + p / 100).

Step-by-Step Solution:
Let the initial salaries be 4x, 5x and 6x for Karthik, Arun and Akhil respectively. Karthik gets 50 percent extra, so new salary of Karthik = 4x * 1.5 = 6x. Arun gets 60 percent extra, so new salary of Arun = 5x * 1.6 = 8x. Akhil gets 50 percent extra, so new salary of Akhil = 6x * 1.5 = 9x. So new salaries in the order Karthik : Arun : Akhil are 6x : 8x : 9x. We need the ratio Akhil : Arun : Karthik, which is 9x : 8x : 6x. Cancel x to obtain 9 : 8 : 6.

Verification / Alternative check:
We can pick a simple value like x = 1000. Then initial salaries are 4000, 5000 and 6000. After the increases: Karthik gets 6000, Arun gets 8000 and Akhil gets 9000. Writing them in the requested order Akhil : Arun : Karthik gives 9000 : 8000 : 6000. Dividing through by 1000 yields 9 : 8 : 6, confirming the ratio derived algebraically.

Why Other Options Are Wrong:
Option 6 : 8 : 9 is the ratio Karthik : Arun : Akhil, not the requested Akhil : Arun : Karthik. Options 8 : 6 : 9, 6 : 5 : 4 and 9 : 6 : 8 do not match any proper reordering of the computed new salaries. They either confuse the order or misapply the percentage increases.

Common Pitfalls:
Students often forget that the question changes the order of names in the final ratio. Another error is to add the same percentage to every term or to treat the ratio numbers directly as percentages. The correct method is to multiply each term by its respective multiplying factor and only then form the ratio.

Final Answer:
The new ratio of the salaries of Akhil, Arun and Karthik is 9 : 8 : 6.