Rs. 94000 is divided among A, B and C such that 20% of A's share = 25% of B's share = 15% of C's share. What is the share (in Rs.) ofC?

Options

A. 23500
B. 29500
C. 40000
D. 42000

Answer

To solve the problem step by step, we will follow the given conditions and find the shares of A, B, and C.

### Step 1: Set up the equations based on the given conditions.
We know that:
- 20% of A's share = 25% of B's share = 15% of C's share.

Let A's share be \( A \), B's share be \( B \), and C's share be \( C \). We can express the relationships as:
\[ 0.2A = 0.25B = 0.15C \]

### Step 2: Express A, B, and C in terms of a common variable.
Let \( k \) be the common value such that:
\[ 0.2A = k \quad \Rightarrow \quad A = \frac{k}{0.2} = 5k \]
\[ 0.25B = k \quad \Rightarrow \quad B = \frac{k}{0.25} = 4k \]
\[ 0.15C = k \quad \Rightarrow \quad C = \frac{k}{0.15} = \frac{20k}{3} \]

### Step 3: Find the total share of A, B, and C.
Now we can express the total share as:
\[ A + B + C = 5k + 4k + \frac{20k}{3} \]

To combine these, we need a common denominator. The common denominator for 1 and 3 is 3:
\[ A + B + C = \frac{15k}{3} + \frac{12k}{3} + \frac{20k}{3} = \frac{47k}{3} \]

### Step 4: Set the total equal to Rs. 94,000.
According to the problem, the total amount is Rs. 94,000:
\[ \frac{47k}{3} = 94000 \]

### Step 5: Solve for k.
To find \( k \), multiply both sides by 3:
\[ 47k = 94000 \times 3 \]
\[ 47k = 282000 \]
Now, divide by 47:
\[ k = \frac{282000}{47} = 6000 \]

### Step 6: Calculate the share of C.
Now that we have \( k \), we can find C's share:
\[ C = \frac{20k}{3} = \frac{20 \times 6000}{3} = \frac{120000}{3} = 40000 \]

### Final Answer:
The share of C is Rs. 40,000.

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