To find the total sales made by Manoj, let's analyze the situation step-by-step:

1. Manoj's commission structure is as follows:
   • \(10\%\) commission on sales up to Rs. 10,000
   • \(5\%\) commission on sales exceeding Rs. 10,000
2. Manoj remits Rs. 75,500 to his company. This amount is after deducting his commission. Let the total sales be denoted by \(x\).
3. Let's break this into scenarios:
   • If the sales are more than Rs. 10,000, then:
     • On the first Rs. 10,000, Manoj gets a commission of \(10\% \times 10,000 = 1,000\)
     • On the remaining amount, which is \((x - 10,000)\), he gets \(5\% \times (x - 10,000)\)
4. The total commission he earns would be: \(1,000 + 0.05(x - 10,000)\)
5. After deducting his commission, he remits Rs. 75,500. Therefore, we can write: \(x - (1,000 + 0.05(x - 10,000)) = 75,500\)
6. Now, simplify the equation:
   • First, calculate the commission part: \(1,000 + 0.05(x - 10,000)\)
   • Distributing inside the parenthesis: \(1,000 + 0.05x - 500\)
   • Simplify further: \(0.05x + 500\)
7. Replacing this in the equation: \(x - (0.05x + 500) = 75,500\)
8. Simplify:
   • \(x - 0.05x - 500 = 75,500\)
   • \(0.95x - 500 = 75,500\)
   • Add 500 to both sides: \(0.95x = 76,000\)
   • Divide both sides by 0.95: \(x = \frac{76,000}{0.95}\)
   • Solving for \(x\) gives: \(x = 80,000\)
9. Thus, the total sales come out to be Rs. 80,000.
10. Verification of Options:
    • Rs. 78,000: This would result in a commission of Rs. 1,400 which doesn't match the scenario because it's less than the needed remittance.
    • Rs. 80,000: As calculated, this matches.
    • Rs. 85,000 and Rs. 90,000: Both options result in a higher commission than what would allow for Rs. 75,500 to be remitted.

Hence, the correct answer is Rs. 80,000.