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

Approach: Whenever shares are described as "percent of the total" then "percent of the remaining", just assume the total is 100 and walk down the line — the leftover after the last named share is automatically R's portion.

Step 1: P's share.
Take total \(=100\). P gets 20% \(\Rightarrow 20\). Remaining \(=80\).

Step 2: M's share.
M gets 40% of the remaining 80 \(\Rightarrow 0.40\times80 = 32\). Remaining \(=80-32=48\).

Step 3: S's share.
"20% less than M" means \(80\%\) of M \(\Rightarrow 0.80\times32 = 25.6\). Remaining \(=48-25.6 = 22.4\).

Step 4: R's share.
R takes whatever is left \(=22.4\).

Step 5: Form the ratio.
\[ P:R = 20 : 22.4 = 200 : 224 = 25 : 28. \]
(Divide by 8: \(200/8=25,\ 224/8=28\).)

Final answer: 25 : 28 — option (A).

Answer 2

Approach: Pick a smart total instead of 100, a number that makes every step a whole number with no decimals at all – here, 125 (a multiple of both 5 and 25).

Step 1: P's share. Take total \(=125\). P gets 20% \(\Rightarrow 25\). Remaining \(=100\).

Step 2: M's share. M gets 40% of 100 \(\Rightarrow 40\). Remaining \(=100-40=60\).

Step 3: S's share. "20% less than M" \(=80\%\) of 40 \(\Rightarrow 32\). Remaining \(=60-32=28\).

Step 4: R's share. R takes what is left \(=28\).

Step 5: Ratio. \[ P:R = 25:28. \]

Final Answer: 25:28 – every number came out whole, with no decimals to simplify at the end.