Question

There are 4 people M, S, P, R.
P gets 20% of the total.
M gets 40% of the remaining amount.
S gets 20% less than M.
R gets the remaining amount.
Find the ratio P : R.

• A. 25 : 28
• B. 12:15
• C. 23:27
• D. 17:19

Hint:

In sequential percentage problems, always be careful about what the percentage is based on – the original total or the "remaining" amount. Assuming a total of 100 makes calculations much simpler.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem describes a sequential distribution of a total amount among four people. We are given the share of each person as a percentage of either the total amount or a remaining amount. The goal is to find the ratio of the shares received by P and R.
Step 2: Key Formula or Approach:
The most straightforward method to solve problems involving percentages of a whole is to assume the total amount is a convenient number, such as 100. This allows us to easily calculate the absolute share of each person and then find the required ratio.
Step 3: Detailed Explanation:
Let the total amount be 100 units. We will calculate the share of each person step-by-step.
1. P's Share:
P gets 20% of the total amount.
\[ \text{P's share} = 20% \text{ of } 100 = 0.20 \times 100 = 20 \text{ units} \] Amount remaining after P's share = \(100 - 20 = 80\) units.
2. M's Share:
M gets 40% of the remaining amount (which is 80 units).
\[ \text{M's share} = 40% \text{ of } 80 = 0.40 \times 80 = 32 \text{ units} \] Amount remaining after M's share = \(80 - 32 = 48\) units.
3. S's Share:
S gets 20% less than M. This means S gets \(100% - 20% = 80%\) of M's share.
\[ \text{S's share} = 80% \text{ of M's share} = 0.80 \times 32 = 25.6 \text{ units} \] Amount remaining after S's share = \(48 - 25.6 = 22.4\) units.
4. R's Share:
R gets the final remaining amount.
\[ \text{R's share} = 22.4 \text{ units} \] Now, we find the ratio of P's share to R's share.
\[ P : R = 20 : 22.4 \] To simplify the ratio and remove the decimal, we can multiply both sides by 10:
\[ P : R = 200 : 224 \] Now, we simplify this ratio by dividing by their greatest common divisor. Let's divide by common factors.
Divide by 4: \(50 : 56\)
Divide by 2: \(25 : 28\)
The simplified ratio is 25:28.
Step 4: Final Answer:
The ratio P : R is 25 : 28.