Let the number of coins received by Brij, Purab, and Mohan be \( x \), \( y \), and \( z \) respectively. According to the problem, the total number of coins is 2505:
\[ x + y + z = 2505 \]
After Brij sells 30 coins, Purab donates 30 coins, and Mohan loses 25 coins, the remaining coins with them are \( x - 30 \), \( y - 30 \), and \( z - 25 \), and the ratio of their coins is given as:
\[ \frac{x - 30}{y - 30} = \frac{46}{41}, \quad \frac{y - 30}{z - 25} = \frac{41}{34} \]
From the first ratio:
\[ \frac{x - 30}{y - 30} = \frac{46}{41} \]
Cross-multiply:
\[ 41(x - 30) = 46(y - 30) \]
Simplifying:
\[ 41x - 1230 = 46y - 1380 \]
\[ 41x - 46y = -150 \]
This is equation (1).
From the second ratio:
\[ \frac{y - 30}{z - 25} = \frac{41}{34} \]
Cross-multiply:
\[ 34(y - 30) = 41(z - 25) \]
Simplifying:
\[ 34y - 1020 = 41z - 1025 \]
\[ 34y - 41z = -5 \]
This is equation (2).
We now solve the system of equations:
\[ 41x - 46y = -150 \quad \text{(1)} \]
\[ 34y - 41z = -5 \quad \text{(2)} \]
From equation (1), solve for \( x \) in terms of \( y \):
\[ x = \frac{46y - 150}{41} \]
Substitute this value of \( x \) into the total number of coins equation:
\[ \frac{46y - 150}{41} + y + z = 2505 \]
Multiply through by 41 to eliminate the denominator:
\[ 46y - 150 + 41y + 41z = 2505 \times 41 \]
Simplify:
\[ 87y + 41z = 102855 \]
Use equation (2) to express \( z \) in terms of \( y \):
\[ 41z = 34y + 5 \quad \Rightarrow \quad z = \frac{34y + 5}{41} \]
Substitute \( z \) into the equation \( 87y + 41z = 102855 \):
\[ 87y + 41\left(\frac{34y + 5}{41}\right) = 102855 \]
Simplify:
\[ 87y + 34y + 5 = 102855 \]
\[ 121y + 5 = 102855 \]
Subtract 5 from both sides:
\[ 121y = 102850 \]
Solve for \( y \):
\[ y = \frac{102850}{121} = 850 \]
Thus, Purab received 850 coins from his father.