Understanding the Ratio Problem

The question asks us to divide a total amount of Rs. 156 into four parts based on a given ratio of 1 : 2 : 4 : 5. This means that for every 1 part the first person (or category) gets, the second gets 2 parts, the third gets 4 parts, and the fourth gets 5 parts.

To solve this kind of ratio problem, we first need to find the total number of 'parts' that the whole amount is being divided into. We do this by summing up the individual numbers in the ratio.

Calculating the Total Ratio Parts

The given ratio is 1 : 2 : 4 : 5.

Sum of the ratio parts \( = 1 + 2 + 4 + 5 \)

Sum of the ratio parts \( = 12 \)

So, the total amount of Rs. 156 is being divided into 12 equal parts.

Determining the Value of One Ratio Part

The total amount is Rs. 156, and this corresponds to 12 ratio parts. To find the value of one ratio part, we divide the total amount by the total number of ratio parts.

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

Value of one ratio part \( = \frac{156}{12} \)

Value of one ratio part \( = 13 \)

So, each 'part' in the ratio is equal to Rs. 13.

Calculating Each Share

Now that we know the value of one ratio part (Rs. 13), we can calculate the amount for each part of the ratio by multiplying the individual ratio number by this value.

• First part: \( 1 \times 13 = 13 \)
• Second part: \( 2 \times 13 = 26 \)
• Third part: \( 4 \times 13 = 52 \)
• Fourth part: \( 5 \times 13 = 65 \)

The rupees in the respective ratios are 13, 26, 52, and 65.

Verifying the Calculation

To check if our calculation is correct, we can add up the calculated shares. They should sum up to the original total amount, which is Rs. 156.

Sum of shares \( = 13 + 26 + 52 + 65 \)

Sum of shares \( = 39 + 52 + 65 \)

Sum of shares \( = 91 + 65 \)

Sum of shares \( = 156 \)

The sum matches the original total amount (Rs. 156), so our calculated shares are correct.

Comparing with Options

We calculated the shares to be 13, 26, 52, and 65. Let's look at the given options:

Comparing our calculated values (13, 26, 52, 65) with the options, we see that Option C matches our results.

Conclusion on Dividing Rs. 156 in Ratio

When Rs. 156 is divided in the ratio 1 : 2 : 4 : 5, the respective amounts are Rs. 13, Rs. 26, Rs. 52, and Rs. 65.

Revision Table: Ratio Calculations

Additional Information: Ratio and Proportion Concepts

Ratios are used to compare quantities of the same kind. They can be simplified like fractions. For example, the ratio 2 : 4 is equivalent to 1 : 2.

Proportion is an equality between two ratios. If \( a : b = c : d \), then a, b, c, and d are in proportion. This can be written as \( \frac{a}{b} = \frac{c}{d} \). The product of the extremes (a and d) is equal to the product of the means (b and c), i.e., \( ad = bc \).

Ratio and proportion problems appear frequently in quantitative aptitude tests and real-life situations involving sharing, scaling, mixing, etc.