700 is divided among A, B, C in such a way that the ratio of the amounts of A and B is 2 : 3 and that of B and C is 4: 5. Find the amounts in each received, in the order A, B, C.
700 को A, B, C के बीच इस प्रकार विभाजित किया जाता है कि A और B की राशि का अनुपात 2:3 है और B तथा C की राशि का अनुपात 4:5 है। A, B, C के क्रम में प्रत्येक को प्राप्त राशि र में ज्ञात कीजिए।

Options

A. A)150,250,300
B. B)160,240,300
C. C)150,250,290
D. D)150,240,310

Explanation

To solve the problem of dividing 700 among A, B, and C based on the given ratios, we can follow these steps:

### Step 1: Understand the Ratios
We are given two ratios:
1. The ratio of A to B is 2:3.
2. The ratio of B to C is 4:5.

### Step 2: Express the Ratios in Terms of a Common Variable
Let’s denote:
- A's amount as \( 2x \)
- B's amount as \( 3x \) (from the first ratio)
- C's amount as \( y \)

From the second ratio (B to C), we can express C in terms of B:
- Since B is \( 3x \) and the ratio of B to C is 4:5, we can set up the equation:
\[ \frac{3x}{y} = \frac{4}{5} \]
Cross-multiplying gives us:
\[ 5 \cdot 3x = 4y \implies 15x = 4y \implies y = \frac{15x}{4} \]

### Step 3: Combine the Expressions
Now we have:
- A = \( 2x \)
- B = \( 3x \)
- C = \( \frac{15x}{4} \)

### Step 4: Set Up the Total Amount Equation
The total amount is given as 700:
\[ 2x + 3x + \frac{15x}{4} = 700 \]

### Step 5: Simplify the Equation
To combine the terms, convert \( 2x \) and \( 3x \) to have a common denominator:
\[ 2x = \frac{8x}{4}, \quad 3x = \frac{12x}{4} \]
Thus, the equation becomes:
\[ \frac{8x}{4} + \frac{12x}{4} + \frac{15x}{4} = 700 \]
Combining the fractions gives:
\[ \frac{35x}{4} = 700 \]

### Step 6: Solve for x
Multiply both sides by 4 to eliminate the fraction:
\[ 35x = 2800 \]
Now, divide by 35:
\[ x = \frac{2800}{35} = 80 \]

### Step 7: Calculate A, B, and C
Now that we have \( x \), we can find the amounts:
- A = \( 2x = 2 \times 80 = 160 \)
- B = \( 3x = 3 \times 80 = 240 \)
- C = \( \frac{15x}{4} = \frac{15 \times 80}{4} = 300 \)

### Final Amounts
Thus, the amounts received by A, B, and C are:
- A = 160
- B = 240
- C = 300

### Summary of Results
The amounts in order A, B, C are:
- A: 160
- B: 240
- C: 300

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