A man invested 1/3 of his retirement gratuity at 6% simple interest: 1/4 of his gratuity at 7% and the rest at 8% simple interest. If his annual return on these investments is 7012)5, find the total amount of gratuity invested by the man.

The correct option is 99,000.

Step-by-step derivation:

Let the total amount of retirement gratuity invested by the man be represented by $G$.

According to the problem, the gratuity is divided into three parts and invested at different simple interest rates:
1. First part: $\frac{1}{3}$ of the gratuity is invested at 6% simple interest.
2. Second part: $\frac{1}{4}$ of the gratuity is invested at 7% simple interest.
3. Third part: The remaining ("rest") of the gratuity is invested at 8% simple interest.

First, let us calculate the fraction of the gratuity that makes up the third part (the rest):
$\text{Remaining fraction}=1-\left(\frac{1}{3}+\frac{1}{4}\right)$

To add the fractions, find a common denominator, which is 12:
$\text{Remaining fraction}=1-\left(\frac{4}{12}+\frac{3}{12}\right)=1-\frac{7}{12}=\frac{5}{12}$

The annual return on these investments is given as 7,012.5 (where "7012)5" is a typographical error for 7,012.50). Using the formula for simple interest for 1 year, $\text{Interest}=\text{Principal}\times \text{Rate}$, we can write the equation for total annual interest as:
$\left(\frac{1}{3}G\times \frac{6}{100}\right)+\left(\frac{1}{4}G\times \frac{7}{100}\right)+\left(\frac{5}{12}G\times \frac{8}{100}\right)=7012.5$

Simplify each term:
$\left(\frac{2}{100}G\right)+\left(\frac{7}{400}G\right)+\left(\frac{40}{1200}G\right)=7012.5$

Express all fractions with a common denominator of 1200:
$\frac{24G}{1200}+\frac{21G}{1200}+\frac{40G}{1200}=7012.5$

Combine the numerators:
$\frac{24G+21G+40G}{1200}=7012.5$

Simplify the numerator:
$\frac{85G}{1200}=7012.5$

Solve for $G$:
$85G=7012.5\times 1200$

Multiply the values on the right side:
$85G=8415000$

Divide by 85 to find the total investment:
$G=\frac{8415000}{85}$

$G=99000$

Thus, the total amount of retirement gratuity invested by the man is 99,000.