A sum of money is to be divided equally among P, Q and R in the respective ratio of 5 : 6 : 7 and another sum of money is to be divided between S and T equally. If S got X 2100 less than P, then how much amount did Q receive?

Options

A. X 2500
B. X 2000
C. X 1500
D. Couldn't be determined

Answer

To solve the problem step by step, we need to break down the information given and use the ratios provided.

### Step 1: Understand the Ratios
The amounts received by P, Q, and R are in the ratio of 5:6:7. This means:
- Let the amount received by P be \( 5x \)
- Let the amount received by Q be \( 6x \)
- Let the amount received by R be \( 7x \)

### Step 2: Calculate the Total Ratio
The total parts of the ratio can be calculated as follows:
\[ 5 + 6 + 7 = 18 \]
This means the total amount can be divided into 18 parts.

### Step 3: Relate S's Amount to P's Amount
According to the problem, S received \( 2100 \) less than P. Therefore, we can express S's amount as:
\[ S = P - 2100 = 5x - 2100 \]
Since S and T share another sum of money equally, T also receives the same amount as S.

### Step 4: Express T's Amount
Since S and T receive equal amounts, we can write:
\[ T = S = 5x - 2100 \]

### Step 5: Find Q's Amount
Now, we need to find out how much Q received. From our earlier expression, we know:
\[ Q = 6x \]

### Step 6: Determine the Value of x
To find the value of \( x \), we need to consider the total amount of money that is being divided among P, Q, R, S, and T. However, since we don't have the total amount, we can express the relationship:
\[ S + T = 2(5x - 2100) \]
This is the total amount received by S and T.

### Step 7: Substitute and Solve
Since we don't have the total amount, we can only express Q's amount in terms of \( x \):
\[ Q = 6x \]

### Step 8: Final Calculation
To find the amount Q received, we need to determine \( x \) from the relationship we established. However, without additional information about the total amount or the specific amounts received by P, Q, or R, we cannot find a numerical value for \( Q \).

### Conclusion
Thus, the amount received by Q is expressed as:
\[ Q = 6x \]
To find the exact amount, we would need the total sum of money or the amount received by P.