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: Express P, M, S, R as decimal fractions of the total \(T\): \(P=0.2T\), \(M=0.4(0.8T)=0.32T\), \(S=0.8(0.32T)=0.256T\), so \(R = T - 0.2T - 0.32T - 0.256T = 0.224T\).
Step 2: Instead of computing P and R separately and simplifying, take the ratio of the coefficients directly:
\[ \frac{R}{P} = \frac{0.224}{0.2} = 1.12 = \frac{28}{25}. \]
Step 3: So \(P:R = 25:28\).
\[ \boxed{25:28} \]
Final Answer: 25:28.