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

To solve the problem of the amounts received by Pinu, Meena, Rinu, and Seema, let's break it down step-by-step:

1. Let the total amount be \(x\).
2. Pinu receives 20% of the total amount, so: \(\text{Amount received by Pinu} = \frac{20}{100} \times x = 0.2x\)
3. After Pinu receives his share, the remaining amount is: \(x - 0.2x = 0.8x\)
4. Meena receives 40% of the remaining amount, thus: \(\text{Amount received by Meena} = \frac{40}{100} \times 0.8x = 0.32x\)
5. Seema receives 20% less than Pinu, which means: \(\text{Amount received by Seema} = 0.8 \times 0.2x = 0.16x\)
6. Now, we find Rinu's share. The total amount is distributed among the four persons, so: \(\text{Amount received by Rinu} = x - (0.2x + 0.32x + 0.16x) = x - 0.68x = 0.32x\)
7. Finally, determine the ratio of the amounts received by Pinu and Rinu: \(\frac{0.2x}{0.32x} = \frac{20}{32} = \frac{5}{8}\)

Therefore, the ratio of the amounts received by Pinu and Rinu is \(5 : 8\), which matches with the correct answer provided:

\(5 : 8\)

 

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 \(5 : 8\).