Question

\(40\%\) of \(70\%\) of P is same as \(35\%\) of \(R\%\) of Q. Also,\(P\%\) of \(P\%\)of 400 is 16. What is the product of P, Q and R?

• A. 32000
• B. 1600
• C. 16000
• D. 320

Answer 1

The Correct Option is A

Product of P, Q, and R Calculation

- We are given the equation: 

\[ 40\% \text{ of } 70\% \text{ of } P = 35\% \text{ of } R\% \text{ of } Q \]

- Additionally, we know:

\[ P\% \text{ of } P\% \text{ of } 400 = 16 \]

Step 1: Solve for \( P \)

Express the second equation as:

\[ \frac{P}{100} \times \frac{P}{100} \times 400 = 16 \]

Simplifying:

\[ \frac{P^2}{10000} \times 400 = 16 \] \[ \frac{P^2}{25} = 16 \] \[ P^2 = 400 \implies P = 20 \]

Step 2: Substitute \( P = 20 \) into the first equation

The first equation becomes:

\[ 40\% \times 70\% \times 20 = 35\% \times R\% \times Q \]

Converting percentages to decimals:

\[ 0.4 \times 0.7 \times 20 = 0.35 \times \frac{R}{100} \times Q \]

Simplifying:

\[ 0.4 \times 0.7 \times 20 = 5.6 \] \[ 5.6 = 0.35 \times \frac{R \times Q}{100} \]

Multiplying both sides by 100:

\[ 560 = 0.35 \times R \times Q \]

Dividing both sides by 0.35:

\[ R \times Q = 1600 \]

Step 3: Calculate the product of \( P \), \( Q \), and \( R \)

The product is:

\[ P \times Q \times R = 20 \times 1600 = 32,000 \]

Conclusion: The product of \( P \), \( Q \), and \( R \) is 32,000.