Mr. Shrimat inherits 2505 gold coins and divids them among his three sons : Bharat, Parat and Marat : in a certain ratio. Out of the total coins received by each of them, Bharat sells 30 coins, Parat donates his 30 coins and Marat losses 25 coins. Now the ratio of gold cois with them is 46 : 41 : 34 respectively. How many coins did Parat receive from his father ?

Options

A. 705
B. 950
C. 800
D. 850

Answer

To solve the problem step by step, we need to determine how many coins each son received from Mr. Shrimat and specifically find out how many coins Parat received.

### Step 1: Set up the equation based on the given ratios and losses
Let the amounts of gold coins received by Bharat, Parat, and Marat be represented as:
- Bharat: \( B \)
- Parat: \( P \)
- Marat: \( M \)

According to the problem, the ratio of the coins after their respective actions is given as:
- Bharat sells 30 coins: \( B - 30 \)
- Parat donates 30 coins: \( P - 30 \)
- Marat loses 25 coins: \( M - 25 \)

The new ratio is:
\[ B - 30 : P - 30 : M - 25 = 46 : 41 : 34 \]

### Step 2: Express the amounts in terms of a variable
We can express the amounts in terms of a common variable \( k \):
\[ B - 30 = 46k \\ P - 30 = 41k \\ M - 25 = 34k \]

### Step 3: Rewrite the equations for \( B \), \( P \), and \( M \)
From the above equations, we can express \( B \), \( P \), and \( M \) as:
\[ B = 46k + 30 \\ P = 41k + 30 \\ M = 34k + 25 \]

### Step 4: Set up the total coins equation
According to the problem, the total number of coins is 2505:
\[ B + P + M = 2505 \]
Substituting the expressions for \( B \), \( P \), and \( M \):
\[ (46k + 30) + (41k + 30) + (34k + 25) = 2505 \]

### Step 5: Combine like terms
Combining the terms gives us:
\[ 46k + 41k + 34k + 30 + 30 + 25 = 2505 \\ 121k + 85 = 2505 \]

### Step 6: Solve for \( k \)
Now, isolate \( k \):
\[ 121k = 2505 - 85 \\ 121k = 2420 \\ k = \frac{2420}{121} \\ k = 20 \]

### Step 7: Calculate the amounts for each son
Now that we have \( k \), we can find the amounts for each son:
- Bharat:
\[ B = 46k + 30 = 46(20) + 30 = 920 + 30 = 950 \]
- Parat:
\[ P = 41k + 30 = 41(20) + 30 = 820 + 30 = 850 \]
- Marat:
\[ M = 34k + 25 = 34(20) + 25 = 680 + 25 = 705 \]

### Step 8: Conclusion
Thus, the number of coins Parat received from his father is:
\[ \boxed{850} \]