P is 20% more than Q and 40% less than R. If value of Q is Rs.150, then what is the value of R.(in Rs.)?

Options

A. 300
B. 320
C. 220
D. 250

Answer

To solve the problem step by step, we will follow the relationships given in the question.

### Step 1: Understand the relationships
We know:
- P is 20% more than Q.
- P is 40% less than R.
- The value of Q is Rs. 150.

### Step 2: Calculate the value of P
Since P is 20% more than Q, we can express P in terms of Q:
\[ P = Q + 20\% \text{ of } Q \]
This can be rewritten as:
\[ P = Q + \frac{20}{100} \times Q \]
\[ P = Q \left(1 + \frac{20}{100}\right) \]
\[ P = Q \left(\frac{120}{100}\right) \]
\[ P = \frac{120}{100} \times Q \]
Substituting the value of Q (Rs. 150):
\[ P = \frac{120}{100} \times 150 \]
\[ P = 1.2 \times 150 \]
\[ P = 180 \]

### Step 3: Express R in terms of P
Now, since P is 40% less than R, we can express R in terms of P:
\[ P = R - 40\% \text{ of } R \]
This can be rewritten as:
\[ P = R \left(1 - \frac{40}{100}\right) \]
\[ P = R \left(\frac{60}{100}\right) \]
\[ P = \frac{60}{100} \times R \]
Now, we can express R in terms of P:
\[ R = \frac{100}{60} \times P \]
\[ R = \frac{5}{3} \times P \]

### Step 4: Substitute the value of P to find R
Now substitute the value of P (Rs. 180) into the equation for R:
\[ R = \frac{5}{3} \times 180 \]
\[ R = 5 \times 60 \]
\[ R = 300 \]

### Final Answer
The value of R is Rs. 300.

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