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The sum of Rs. 9900 is divided among A, ...

The sum of Rs. 9900 is divided among A, B and C such that B gets 2/3 of A and C. C gets 3/8 of A and B. Then they get separately?

A

`3900, 3300, 2700`

B

`3960, 3200, 2740`

C

`3960, 3240, 2700`

D

`3000, 3200, 2700`

Text Solution

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The correct Answer is:
To solve the problem of dividing Rs. 9900 among A, B, and C based on the given conditions, we can follow these steps: ### Step 1: Set up the equations based on the problem statement. Let: - A's share = A - B's share = B - C's share = C From the problem, we have the following relationships: 1. The total amount is given by: \[ A + B + C = 9900 \quad \text{(Equation 1)} \] 2. B gets \( \frac{2}{3} \) of A and C: \[ B = \frac{2}{3}(A + C) \quad \text{(Equation 2)} \] 3. C gets \( \frac{3}{8} \) of A and B: \[ C = \frac{3}{8}(A + B) \quad \text{(Equation 3)} \] ### Step 2: Substitute Equation 2 into Equation 1. From Equation 2, we can express \( A + C \) in terms of B: \[ A + C = \frac{3}{2}B \] Substituting this into Equation 1 gives: \[ A + \frac{2}{3}(A + C) + C = 9900 \] Substituting \( A + C = \frac{3}{2}B \): \[ B + \frac{3}{2}B = 9900 \] Combining terms: \[ \frac{5}{2}B = 9900 \] ### Step 3: Solve for B. To find B, multiply both sides by \( \frac{2}{5} \): \[ B = \frac{2}{5} \times 9900 = 3960 \] ### Step 4: Substitute B back into Equation 2 to find A and C. Now that we have B, we can find A and C. Substitute B into Equation 2: \[ A + C = \frac{3}{2} \times 3960 = 5940 \] Now we have: \[ A + C = 5940 \quad \text{(Equation 4)} \] ### Step 5: Substitute B into Equation 3 to find C. Now substitute B into Equation 3: \[ C = \frac{3}{8}(A + 3960) \] Substituting \( A + C = 5940 \) into this gives: \[ C = \frac{3}{8}(5940 - C + 3960) \] This simplifies to: \[ C = \frac{3}{8}(9900 - C) \] Multiplying both sides by 8: \[ 8C = 3(9900 - C) \] Expanding and combining terms: \[ 8C + 3C = 29700 \] \[ 11C = 29700 \] \[ C = \frac{29700}{11} = 2700 \] ### Step 6: Find A using Equation 4. Now substitute C back into Equation 4: \[ A + 2700 = 5940 \] \[ A = 5940 - 2700 = 3240 \] ### Final Shares: - A's share = Rs. 3240 - B's share = Rs. 3960 - C's share = Rs. 2700 ### Summary: Thus, the final amounts received by A, B, and C are: - A = Rs. 3240 - B = Rs. 3960 - C = Rs. 2700
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