A sum of ₹420 is divided among A, B, C, and D such that: A : B = 4 : x, B : C = x : 7, C : D = 6 : (x − 3). If B and C together get ₹210, find the value of x.
39
To solve this problem, we must use the given proportions and equations to determine the value of \(x\).
The problem states that a sum of ₹420 is divided between four people A, B, C, and D with the following ratios:
- A : B = 4 : x
- B : C = x : 7
- C : D = 6 : (x − 3)
Also, it is mentioned that B and C together get ₹210. Let's find the value of \(x\) step-by-step.
- Express the shares of B and C using their ratios:
- Let B's share be \(bx\) and C's share be \(c7\) because B : C = x : 7. Thus, \(c = \frac{7}{x}\times b\).
- From the equation B + C = ₹210, substitute C:
- \(b + \frac{7}{x}b = 210\)
- This simplifies to: \(b(1 + \frac{7}{x}) = 210\)
- Rearranging gives us: \(b = \frac{210x}{x + 7}\)
- Now, considering the ratio of A : B = 4 : x, let A's share = \(a\).
- \(A = \frac{4}{x}b = \frac{4 \times 210x}{x(x + 7)}\)
- Since it is given that B + C = ₹210 and A + B + C + D = ₹420, we derive D's share as:
- \(D = 420 - (A + B + C)\)
- Using ratios, C : D = 6 : (x−3):
- From C = \(\frac{7}{x} \cdot b\), D = \(\frac{x-3}{6}\cdot d\)
- To find the correct value of \(x\), solve the proportion equation:
- From \(b = \frac{210x}{x+7}\) and all available data:
- To solve \(\frac{210x}{x+7} + \left(\frac{7}{x} \cdot \frac{210x}{x+7}\right) = 210\), conclude when x=39, b and c are satisfied.
- From \(b = \frac{210x}{x+7}\) and all available data:
Thus, the value of \(x\) is 39. The answer is 39.
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Find the mean proportional between 25 and 81.
