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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:

  1. C's share is Rs 120 more than A's share: 
    \(Kx = 3x + 120\)
  2. B's share is Rs 30 less than A's share: 
    \(2x = 3x - 30\)

We tackle each equation separately:

  1. From the second equation: 
    \(2x = 3x - 30 \Rightarrow 3x - 2x = 30 \Rightarrow x = 30\)
  2. 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 \( K \):

  1. \(K = \frac{210}{30} = 7\)

Thus, the value of \( K \) is 7.

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Important Questions from Ratio and Proportion (Notes)

  1. 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
  2. A and B started a business with investment of ₹ $60,000$ and ₹ $90,000$ respectively. After 5 months, B left the business and C joined with a capital which is ₹ 60,000 less than that of B. If at the end of the year, the share of C in the profit was ₹ 42,000, then find the total profit earned at the end of the year.

  3. If A exceeds B by 50% and B is less than C by 25%, then A: C is:
  4. दो संख्याएँ A और B इस प्रकार हैं कि A के $5\%$ और B के $4\%$ का योग A के $6\%$ और B के $8\%$ के योग का दो-तिहाई है । A : B का अनुपात ज्ञात कीजिए ।
  5. एक हॉकी टीम ने खेल में 6 जीते और 8 हार गए। जीते गये खेलों की संख्या का अनुपात क्या है ?
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