Rs700 is divided among A, B, C in such a way that the ratio of the amounts of A and B 1s 2 : 3 and that of B and C is 4 : 5. Find the amounts in Rs each received, in the order A, B, C.

Options

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

Answer

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

### Step 1: Understand the Ratios
We have 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 the amounts received by A, B, and C as follows:
- Let A = 2x (from the ratio A:B = 2:3)
- Let B = 3x (from the ratio A:B = 2:3)

Now we need to express C in terms of B. From the ratio B:C = 4:5, we can express C as:
- Let B = 4y (from the ratio B:C = 4:5)
- Let C = 5y (from the ratio B:C = 4:5)

### Step 3: Find a Common Variable
Since B is represented in both ratios, we can set the two expressions for B equal to each other:
3x = 4y

### Step 4: Solve for One Variable
From the equation 3x = 4y, we can express y in terms of x:
y = (3/4)x

### Step 5: Substitute Back to Find A, B, and C
Now we can substitute y back into the expressions for C:
C = 5y = 5 * (3/4)x = (15/4)x

Now we have:
- A = 2x
- B = 3x
- C = (15/4)x

### Step 6: Express the Total Amount
The total amount is given as Rs 700:
A + B + C = 700
Substituting the expressions we found:
2x + 3x + (15/4)x = 700

### Step 7: Combine Like Terms
To combine the terms, we need a common denominator:
(8/4)x + (12/4)x + (15/4)x = 700
(35/4)x = 700

### Step 8: Solve for x
Now, multiply both sides by 4 to eliminate the fraction:
35x = 2800
Now divide by 35:
x = 2800 / 35
x = 80

### Step 9: Calculate A, B, and C
Now that we have the value of x, we can find the amounts for A, B, and C:
- A = 2x = 2 * 80 = 160
- B = 3x = 3 * 80 = 240
- C = (15/4)x = (15/4) * 80 = 300

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

### Summary
The amounts received by A, B, and C in order are Rs 160, Rs 240, and Rs 300.

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