Dividing Money in a Given Ratio

The problem asks us to divide a total amount of Rs. 368 into four parts according to the ratio 1:5:8:9. To do this, we first find the total number of parts in the ratio.

Calculating Total Ratio Parts

The given ratio is 1:5:8:9. The total number of parts is the sum of the individual ratio parts:

\(\text{Total ratio parts} = 1 + 5 + 8 + 9\)

\(\text{Total ratio parts} = 23\)

So, the whole amount Rs. 368 is divided into 23 equal parts.

Calculating the Value of One Ratio Part

Next, we need to find the value of one single ratio part. We do this by dividing the total amount by the total number of ratio parts:

\(\text{Value of one part} = \frac{\text{Total Amount}}{\text{Total ratio parts}}\)

\(\text{Value of one part} = \frac{368}{23}\)

\(\text{Value of one part} = 16\)

Each single ratio part is worth Rs. 16.

Calculating Each Share

Now, we can find the amount for each share by multiplying the value of one part (Rs. 16) by the respective ratio part:

• First share = \(1 \times \text{Value of one part} = 1 \times 16 = \text{Rs. } 16\)
• Second share = \(5 \times \text{Value of one part} = 5 \times 16 = \text{Rs. } 80\)
• Third share = \(8 \times \text{Value of one part} = 8 \times 16 = \text{Rs. } 128\)
• Fourth share = \(9 \times \text{Value of one part} = 9 \times 16 = \text{Rs. } 144\)

The amounts in the respective ratios are Rs. 16, Rs. 80, Rs. 128, and Rs. 144.

Verification of the Shares

To verify if our calculations are correct, we can add up the individual shares to see if they equal the original total amount Rs. 368:

\(\text{Sum of shares} = 16 + 80 + 128 + 144\)

\(\text{Sum of shares} = 96 + 128 + 144\)

\(\text{Sum of shares} = 224 + 144\)

\(\text{Sum of shares} = 368\)

The sum of the calculated shares is Rs. 368, which matches the total amount given in the problem. This confirms our calculation is correct.

Comparing with Options

Let's compare our calculated shares (16, 80, 128, 144) with the given options:

Option C provides the amounts 16, 80, 128, and 144, which exactly match our calculated shares for the ratio 1:5:8:9 when dividing Rs. 368.

Ratio and Proportion Revision Table

Additional Information on Ratio Problems

Ratio problems often involve dividing a quantity into parts proportional to a given ratio. The key steps are always:

• Find the total number of 'ratio units' by summing the parts of the ratio.
• Calculate the value of one ratio unit by dividing the total quantity by the total ratio units.
• Determine each individual share by multiplying the value of one ratio unit by the corresponding number in the ratio.

This method is applicable whether you are dividing money, lengths, weights, or any other quantity based on a given ratio. Always ensure the units are consistent throughout the problem.