If ₹3800 is distributed among A,B, C such that A : B= 1 : 2 and B : C = 3 : 5,the find the share of B.

Options

A. ₹1200
B. ₹2000
C. ₹1400
D. ₹600

Answer

To solve the problem of distributing ₹3800 among A, B, and C based on the given ratios, we can follow these steps:

### Step 1: Understand the Ratios
We are given the ratios:
- A : B = 1 : 2
- B : C = 3 : 5

### Step 2: Express the Ratios in Terms of a Common Variable
Let’s express A, B, and C in terms of a common variable.
- From A : B = 1 : 2, we can say:
- A = 1x
- B = 2x

- From B : C = 3 : 5, we can express B and C as:
- B = 3y
- C = 5y

### Step 3: Equate the Expressions for B
Since B is represented in both ratios, we can set the two expressions for B equal to each other:
\[ 2x = 3y \]

### Step 4: Solve for One Variable in Terms of the Other
From the equation \( 2x = 3y \), we can express y in terms of x:
\[ y = \frac{2x}{3} \]

### Step 5: Substitute Back to Find C
Now substitute y back into the expression for C:
\[ C = 5y = 5 \left( \frac{2x}{3} \right) = \frac{10x}{3} \]

### Step 6: Write the Ratios in Terms of x
Now we have:
- A = 1x
- B = 2x
- C = \( \frac{10x}{3} \)

### Step 7: Find a Common Denominator
To combine these ratios, we can express all terms with a common denominator:
- A = \( \frac{3x}{3} \)
- B = \( \frac{6x}{3} \)
- C = \( \frac{10x}{3} \)

### Step 8: Add the Ratios
Now we can add these fractions together:
\[ A + B + C = \frac{3x}{3} + \frac{6x}{3} + \frac{10x}{3} = \frac{19x}{3} \]

### Step 9: Set the Total Equal to ₹3800
We know that the total amount distributed is ₹3800:
\[ \frac{19x}{3} = 3800 \]

### Step 10: Solve for x
Multiply both sides by 3:
\[ 19x = 11400 \]
Now divide by 19:
\[ x = \frac{11400}{19} = 600 \]

### Step 11: Calculate B's Share
Now that we have the value of x, we can find B's share:
\[ B = 2x = 2 \times 600 = 1200 \]

### Conclusion
Thus, the share of B is ₹1200.

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