Question
A, B and C invested some money in the ratio of 3 : 2 : K. If C's share is Rs 120 more than A's share, B's share is Rs 30 less than A's share, then the value of K is :
The correct answer is
7
To find the value of \( K \) in the investment ratio of A, B, and C, we start by representing their investments mathematically based on the given ratio.
Given that the investments are in the ratio of \( 3 : 2 : K \), let's denote the actual amounts invested by A, B, and C as \( 3x \), \( 2x \), and \( Kx \) respectively, where \( x \) is a common multiplier.
From the problem, we know:
- C's share is Rs 120 more than A's share:
\(Kx = 3x + 120\) - B's share is Rs 30 less than A's share:
\(2x = 3x - 30\)
We tackle each equation separately:
- From the second equation:
\(2x = 3x - 30 \Rightarrow 3x - 2x = 30 \Rightarrow x = 30\) - Substituting \(x = 30\) into the first equation:
\(Kx = 3x + 120\)
Substituting \(x = 30\):
\(K \times 30 = 3 \times 30 + 120\)
\(30K = 90 + 120\)
\(30K = 210\)
Solving for \( K \):
- \(K = \frac{210}{30} = 7\)
Thus, the value of \( K \) is 7.
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Important Questions from Ratio and Proportion (Notes)
- Anand and Deepak started a business investing ₹ 22,500 and ₹ 35,000 respectively. Out of a total profit of ₹ 13,800, Deepak's share is
- If A exceeds B by 50% and B is less than C by 25%, then A: C is:
- For any two numbers p and q,
$(p + q) : (p - q) : pq = 7 : 1 : 60$
If $p^2 + q^2 = r^2$, then r is equal to - If A : B = 5 : 6 and B : C = 6 : 7, then A + B : B + C : A + C is :
- If a number is added to each of the numbers 16, 20 and 30, then the resulting numbers are in the continued proportion. Find the mean proportional between the largest and smallest of the resulting numbers.
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