There are 3 societies A, B, C.A lent cars to B and C as many as they had already.After some time B gave as many tractors to A and C as many as they have. After sometime c did the same thing. At the end of this transaction each one of them had 24.Find the cars each originally had.
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Answer / Shreekant Gupta
Let's denote the number of cars initially owned by A, B, and C as a, b, and c respectively. We know that after transactions, they all have 24 cars each: a + b + c = 72 (because there are 3 of them). Also, we know that B lent cars to both A and C equal to the number of cars initially owned by them (b - a = c) and C gave back the same number of cars as tractors they received from B (c - b = a/2). Solving these equations, we get: a + b + c = 72, b - a = c, and c - b = a/2. From the first equation, we can express a in terms of b and c (a = 72 - b - c). Substituting this expression into the second and third equations, we get: b - a = c => b - (72 - b - c) = c => 2b = 84 - c and c - b = a/2 => c - b = (72 - b - c)/2. Combining these two equations, we get: 3b = 168 - 3c. We have two variables (b and c) and only one equation, so it's impossible to find the exact number of cars originally owned by A, B, and C based on the given information.
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