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What sum of money is divided between A, B, and C if B and C together get Rs. 100 and C and A together get Rs. 150, and A gets twice as much as B?

(a) Rs. 75
(b) Rs. 100
(c) Rs. 125
(d) Rs. 150

1 Answer

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Final answer:

The total sum of money divided between A, B, and C is Rs. 200. This is determined by solving a system of equations based on the information given: B and C together get Rs. 100, C and A together get Rs. 150, and A gets twice as much as B. Therefore, the total sum of money that is divided between A, B, and C is A + B + C = Rs. 100 + Rs. 50 + Rs. 50 = Rs. 200.

Step-by-step explanation:

To find out the sum of money divided between A, B, and C, we can create a system of equations based on the information provided. We know that B and C together get Rs. 100, C and A together get Rs. 150, and A gets twice as much as B. Let's denote the amount that A, B, and C receive with A, B, and C, respectively.

B + C = Rs. 100 (1)
A + C = Rs. 150 (2)
A = 2B (3)

We can use equation (3) to replace A in equation (2) with 2B, which gives us the following:
2B + C = Rs. 150 (4)

Now, we subtract equation (1) from equation (4):

(2B + C) - (B + C) = Rs. 150 - Rs. 100
B = Rs. 50

Using the value of B, we can now find the value of A from equation (3):

A = 2B = 2 × Rs. 50 = Rs. 100

Lastly, using the value of B, we can determine C from equation (1):

C = Rs. 100 - B = Rs. 100 - Rs. 50 = Rs. 50

Therefore, the total sum of money that is divided between A, B, and C is A + B + C = Rs. 100 + Rs. 50 + Rs. 50 = Rs. 200.

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