Question

A certain amount of money was divided among Pinu, Meena, Rinu, and Seema. Pinu received 20% of the total amount and Meena received 40% of the remaining amount. If Seema received 20% less than Pinu, the ratio of the amounts received by Pinu and Rinu is:

• A. \(4 : 5\)
• B. \(5 : 8\)
• C. \(3 : 5\)
• D. \(2 : 3\)

Hint:

In distribution problems, it often helps to assume a convenient total (like 100) when only percentages are involved. This makes computations easy and does not affect the final ratios.

Answer 1

The Correct Option is B

Approach: Percentages of an unknown total are easiest if you just assume a convenient total. Take the whole pot as \(100\) units; every share becomes a plain number and Rinu is whatever is left over.

Step 1: Let the total be \(100\). Pinu gets \(20\%\): \[ \text{Pinu} = 20. \]

Step 2: Remaining after Pinu \(= 100 - 20 = 80\). Meena gets \(40\%\) of this remaining amount: \[ \text{Meena} = 0.40 \times 80 = 32. \]

Step 3: Seema gets \(20\%\) less than Pinu: \[ \text{Seema} = 0.80 \times 20 = 16. \]

Step 4: Rinu takes whatever remains: \[ \text{Rinu} = 100 - (20 + 32 + 16) = 100 - 68 = 32. \]

Step 5: Required ratio \[ \text{Pinu} : \text{Rinu} = 20 : 32 = 5 : 8. \]

Final answer: \(5 : 8\) — option 2.

Answer 2

Step 1: Let the total amount be \(T\). For convenience, take \(T = 100\) (any other positive value would give the same ratio).
Step 2: Pinu’s share. Pinu gets \(20%\) of the total: \[ P = 20% \text{ of } 100 = 20. \]
Step 3: Meena’s share. Amount remaining after Pinu: \[ 100 - 20 = 80. \] Meena gets \(40%\) of this remaining amount: \[ M = 40% \text{ of } 80 = 0.4 \times 80 = 32. \]
Step 4: Seema’s share. Seema receives \(20%\) less than Pinu: \[ S = P - 20% \text{ of } P = 20 - 0.2 \times 20 = 20 - 4 = 16. \]
Step 5: Rinu’s share. Rinu gets the remaining amount: \[ R = 100 - (P + M + S) = 100 - (20 + 32 + 16) = 100 - 68 = 32. \]
Step 6: Required ratio \(P : R\). \[ P : R = 20 : 32. \] Divide both by 4: \[ P : R = 5 : 8. \] Therefore, the ratio of the amounts received by Pinu and Rinu is \(5 : 8\).