Raju invests Rs 6,000 in a scheme. Santhosh invests 30 percent less than Raju, and Rajitha invests 25 percent more than Santhosh. What is the ratio of the amount invested by Rajitha to the total amount invested by all three of them together?

Introduction / Context:
This investment based ratio question is about three people, Raju, Santhosh and Rajitha, investing different amounts in relation to each other. One amount is given explicitly, and the other two are described using percentage increases and decreases. Once we convert all these amounts into actual rupee values, we can compute the ratio of one person investment to the total combined investment.

Given Data / Assumptions:
- Raju invests Rs 6,000.
- Santhosh invests 30 percent less than Raju.
- Rajitha invests 25 percent more than Santhosh.
- We need the ratio of Rajitha investment to the total investment of all three combined.

Concept / Approach:
The approach involves sequential percentage calculations. First, we compute Santhosh investment by reducing Raju amount by 30 percent. Then we use Santhosh amount to calculate Rajitha investment by increasing it by 25 percent. After obtaining all three absolute amounts, we add them to get the total investment. Finally, we express Rajitha amount over the total amount as a simplified ratio with whole number terms.

Step-by-Step Solution:
Step 1: Raju investment = Rs 6,000. Step 2: Santhosh invests 30 percent less than Raju, so Santhosh amount = 6,000 * (1 - 0.30) = 6,000 * 0.70 = Rs 4,200. Step 3: Rajitha invests 25 percent more than Santhosh, so Rajitha amount = 4,200 * (1 + 0.25) = 4,200 * 1.25. Step 4: Compute 4,200 * 1.25 = 4,200 * (5/4) = 4,200 * 5 / 4 = 21,000 / 4 = Rs 5,250. Step 5: Total investment of all three = 6,000 + 4,200 + 5,250 = Rs 15,450. Step 6: Required ratio = Rajitha investment : total investment = 5,250 : 15,450. Step 7: Simplify the ratio by dividing both terms by 150 to get 35 : 103.

Verification / Alternative check:
Alternatively, we can work entirely in relative terms first. Let Raju amount be 6,000 units. Santhosh amount is 70 percent of that, and Rajitha amount is 125 percent of Santhosh amount. That means Rajitha amount is 6,000 * 0.70 * 1.25 which also simplifies to 5,250. This reconfirms the earlier calculation. Re adding the three amounts again gives 15,450, so the ratio 5,250 : 15,450 is consistent.

Why Other Options Are Wrong:
25 : 114, 15 : 108 and 41 : 94 do not reduce to the fraction 5,250 divided by 15,450. When simplified, none of these options represents 35 : 103. Only 35 : 103 maintains the correct proportional relationship between Rajitha share and the total investment after simplification.

Common Pitfalls:
A typical mistake is using the 25 percent increase directly on Raju amount instead of on Santhosh amount. Another common error is miscalculating 30 percent less by subtracting 30 rupees per 1000 instead of 30 percent of the total. There can also be simplification errors when reducing 5,250 : 15,450 to lowest terms. Carefully dividing by a common factor such as 150 helps avoid such issues.

Final Answer:
The ratio of Rajitha investment to the total investment of all three is 35 : 103.