Let the coin counts for Brij, Purab, and Mohan be \( x \), \( y \), and \( z \), respectively. The total number of coins is 2505:
\[ x + y + z = 2505 \]
After transactions: Brij sells 30 coins, Purab donates 30, and Mohan loses 25. The remaining coin counts and their ratio are:
\[ \frac{x - 30}{y - 30} = \frac{46}{41}, \quad \frac{y - 30}{z - 25} = \frac{41}{34} \]
From the first ratio:
\[ \frac{x - 30}{y - 30} = \frac{46}{41} \]
Cross-multiplying:
\[ 41(x - 30) = 46(y - 30) \]
Simplifying:
\[ 41x - 1230 = 46y - 1380 \]
\[ 41x - 46y = -150 \]
Equation (1).
From the second ratio:
\[ \frac{y - 30}{z - 25} = \frac{41}{34} \]
Cross-multiplying:
\[ 34(y - 30) = 41(z - 25) \]
Simplifying:
\[ 34y - 1020 = 41z - 1025 \]
\[ 34y - 41z = -5 \]
Equation (2).
System of equations:
\[ 41x - 46y = -150 \quad \text{(1)} \]
\[ 34y - 41z = -5 \quad \text{(2)} \]
From equation (1), solve for \( x \):
\[ x = \frac{46y - 150}{41} \]
Substitute into the total coins equation:
\[ \frac{46y - 150}{41} + y + z = 2505 \]
Multiply by 41:
\[ 46y - 150 + 41y + 41z = 2505 \times 41 \]
Simplify:
\[ 87y + 41z = 102855 \]
From equation (2), express \( z \) in terms of \( y \):
\[ 41z = 34y + 5 \quad \Rightarrow \quad z = \frac{34y + 5}{41} \]
Substitute \( z \) into \( 87y + 41z = 102855 \):
\[ 87y + 41\left(\frac{34y + 5}{41}\right) = 102855 \]
Simplify:
\[ 87y + 34y + 5 = 102855 \]
\[ 121y + 5 = 102855 \]
Subtract 5:
\[ 121y = 102850 \]
Solve for \( y \):
\[ y = \frac{102850}{121} = 850 \]
Thus, Purab received 850 coins.
| Mutual fund A | Mutual fund B | Mutual fund C | |
| Person 1 | ₹10,000 | ₹20,000 | ₹20,000 |
| Person 2 | ₹20,000 | ₹15,000 | ₹15,000 |
List I | List II | ||
| A. | Duplicate of ratio 2: 7 | I. | 25:30 |
| B. | Compound ratio of 2: 7, 5:3 and 4:7 | II. | 4:49 |
| C. | Ratio of 2: 7 is same as | III. | 40:147 |
| D. | Ratio of 5: 6 is same as | IV. | 4:14 |