P is 10% less than Q. Q is 10% more than R. R is 20% less than S. If S is 1000, then what is the value of P?

Options

A. 648
B. 792
C. 676
D. 736

Answer

To solve the problem step by step, let's break it down:

1. **Identify the value of S**:
We are given that S = 1000.

2. **Calculate R**:
R is 20% less than S.
To find R, we can calculate:
\[ R = S - (20\% \text{ of } S) = S - \frac{20}{100} \times S = S \times \left(1 - \frac{20}{100}\right) = S \times \frac{80}{100} \]
Substituting the value of S:
\[ R = 1000 \times \frac{80}{100} = 1000 \times 0.8 = 800 \]

3. **Calculate Q**:
Q is 10% more than R.
To find Q, we can calculate:
\[ Q = R + (10\% \text{ of } R) = R + \frac{10}{100} \times R = R \times \left(1 + \frac{10}{100}\right) = R \times \frac{110}{100} \]
Substituting the value of R:
\[ Q = 800 \times \frac{110}{100} = 800 \times 1.1 = 880 \]

4. **Calculate P**:
P is 10% less than Q.
To find P, we can calculate:
\[ P = Q - (10\% \text{ of } Q) = Q - \frac{10}{100} \times Q = Q \times \left(1 - \frac{10}{100}\right) = Q \times \frac{90}{100} \]
Substituting the value of Q:
\[ P = 880 \times \frac{90}{100} = 880 \times 0.9 = 792 \]

Thus, the value of P is **792**.