To solve the problem of dividing Rs. 750 among A, B, and C based on the given ratios, we can follow these steps:
### Step 1: Understand the Ratios
We are given two ratios:
1. A : B = 5 : 2
2. B : C = 7 : 13
### Step 2: Express B in terms of A
From the first ratio (A : B = 5 : 2), we can express B in terms of A:
- Let A = 5x and B = 2x, where x is a common multiplier.
### Step 3: Express C in terms of B
From the second ratio (B : C = 7 : 13), we can express C in terms of B:
- Let B = 7y and C = 13y, where y is another common multiplier.
### Step 4: Equate B from both ratios
Since B is expressed in two different ways, we can equate them:
- From A : B, we have B = 2x.
- From B : C, we have B = 7y.
Setting them equal gives us:
\[ 2x = 7y \]
### Step 5: Express x in terms of y
From the equation \( 2x = 7y \), we can express x in terms of y:
\[ x = \frac{7y}{2} \]
### Step 6: Substitute x back to find A, B, and C
Now we can express A, B, and C in terms of y:
- A = 5x = 5 * \(\frac{7y}{2}\) = \(\frac{35y}{2}\)
- B = 2x = 2 * \(\frac{7y}{2}\) = 7y
- C = 13y
### Step 7: Calculate the total share
Now we can find the total share:
\[ A + B + C = \frac{35y}{2} + 7y + 13y \]
To combine these, we convert 7y and 13y to have a common denominator:
\[ 7y = \frac{14y}{2} \]
\[ 13y = \frac{26y}{2} \]
So,
\[ A + B + C = \frac{35y}{2} + \frac{14y}{2} + \frac{26y}{2} = \frac{75y}{2} \]
### Step 8: Set the total equal to Rs. 750
Now we set this equal to the total amount of Rs. 750:
\[ \frac{75y}{2} = 750 \]
### Step 9: Solve for y
To find y, we multiply both sides by 2:
\[ 75y = 1500 \]
Now divide by 75:
\[ y = 20 \]
### Step 10: Find A's share
Now that we have y, we can find A's share:
\[ A = \frac{35y}{2} = \frac{35 * 20}{2} = \frac{700}{2} = 350 \]
Thus, A's share is Rs. 350.
### Final Answer
A's share is **Rs. 350**.
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