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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Important Questions from Ratio and proportion
A sum of Rs. 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6 . What is the difference between the maximum share and the minimum share?
In a class, there are three groups A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight of the students of the class?
How many different sums can be formed with the denominations Rs. 50, Rs. 100, Rs. 200, Rs. 500 and Rs. 2,000 taking at least three denominations at a time?
In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speeds of A to B assuming that both start at the same time?
The monthly incomes of Peter and Paul are in the ratio of 4 : 3. Their expenses are in the ratio of 3 : 2. If each saves Rs. 6,000 at the end of the month, their monthly incomes respectively are (in Rs.)
