Divide Rs. 156 in the ratio 1:2:4:5. The rupees in the respective ratios are given by :
A. 13, 26, 53 & 64
B. 13, 26, 51 & 66
C. 13, 26, 52 & 65
D. 13, 25, 53 & 65

Options

A. B
B. C
C. D
D. A

Answer

To solve the problem of dividing Rs. 156 in the ratio of 1:2:4:5, we can follow these steps:

### Step 1: Understand the Ratio
The ratio 1:2:4:5 means that for every 1 part, there are 2 parts, 4 parts, and 5 parts respectively. We can denote these parts as:
- First part = 1x
- Second part = 2x
- Third part = 4x
- Fourth part = 5x

### Step 2: Calculate the Total Parts
Add the parts of the ratio together:
1 + 2 + 4 + 5 = 12 parts in total.

### Step 3: Set Up the Equation
Since the total amount to be divided is Rs. 156, we can set up the equation:
1x + 2x + 4x + 5x = 156
This simplifies to:
12x = 156

### Step 4: Solve for x
To find the value of x, divide both sides of the equation by 12:
x = 156 / 12
x = 13

### Step 5: Calculate Each Part
Now that we have the value of x, we can calculate each part:
- First part = 1x = 1 * 13 = 13
- Second part = 2x = 2 * 13 = 26
- Third part = 4x = 4 * 13 = 52
- Fourth part = 5x = 5 * 13 = 65

### Step 6: Present the Results
The amounts in the respective ratios are:
- First part: Rs. 13
- Second part: Rs. 26
- Third part: Rs. 52
- Fourth part: Rs. 65

### Conclusion
Thus, the amounts in the respective ratios are Rs. 13, Rs. 26, Rs. 52, and Rs. 65, which corresponds to option C.

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