Divide Rs. 80 among three people in the proportion 3 : 6 : 7. What are the three resulting shares?

Introduction / Context:
This is a basic ratio division question. The total amount of Rs. 80 has to be split among three persons in the ratio 3 : 6 : 7. Such problems are often asked to check whether candidates can correctly convert a ratio into actual numerical parts and ensure that the entire total is exactly distributed.

Given Data / Assumptions:

• Total amount = Rs. 80.
• Ratio of shares = 3 : 6 : 7.
• We need to find each individual share that matches both the ratio and the sum.

Concept / Approach:
If a sum S is divided into parts in the ratio a : b : c, then the sum of the ratio terms is a + b + c. Each part is obtained by multiplying S by the respective ratio term and dividing by the total of the ratio terms. That is, first share = (a / (a + b + c)) * S, second share = (b / (a + b + c)) * S and so on. We apply this directly here with a = 3, b = 6 and c = 7.

Step-by-Step Solution:
Given ratio = 3 : 6 : 7.Total of ratio terms = 3 + 6 + 7 = 16.Total amount S = Rs. 80.Value of one ratio unit = 80 / 16 = 5.First share = 3 * 5 = Rs. 15.Second share = 6 * 5 = Rs. 30.Third share = 7 * 5 = Rs. 35.Therefore, the three shares are Rs. 15, Rs. 30 and Rs. 35.

Verification / Alternative check:
Add the three shares: 15 + 30 + 35 = 80, which matches the original total.Check ratio: 15 : 30 : 35 simplifies to 3 : 6 : 7 when divided by 5, so the division respects the given ratio.

Why Other Options Are Wrong:
Options where the three amounts do not add to Rs. 80 or do not simplify to the ratio 3 : 6 : 7 are incorrect. For example, Rs. 10, Rs. 35 and Rs. 40 sum to 85, not 80. Similarly, Rs. 10, Rs. 40 and Rs. 35 give a total of 85. Only Rs. 15, Rs. 30 and Rs. 35 both sum to 80 and maintain the 3 : 6 : 7 ratio.

Common Pitfalls:
A common error is to treat ratio terms as direct rupee values without scaling them to match the total sum, leading to a mismatch in the final total. Another pitfall is arithmetic mistakes when computing the sum of ratio terms or dividing the total amount. Always compute the unit value as total divided by the sum of ratio terms and then multiply each term by that unit value.

Final Answer:
The three shares are Rs. 15, Rs. 30 and Rs. 35 respectively.