The ratio of the efficiency of P,Q and R is `2:3:5`. The total wages of P,Q and R working for 14, 24 and 20 days, respectively are Rs. 6000. Find the total wages of three, if P works for 9 days, Q for 14 days and R for 8 days.

Options

A. Rs. 3000
B. Rs.2860
C. Rs.2450
D. Rs.3240

Explanation

To solve the problem step by step, we will follow the given information and calculate the required wages.

### Step 1: Determine the daily wages based on efficiency
The efficiency ratio of P, Q, and R is given as 2:3:5. This means:
- P's daily wage = 2x
- Q's daily wage = 3x
- R's daily wage = 5x

### Step 2: Calculate total wages based on days worked
P works for 14 days, Q for 24 days, and R for 20 days. The total wages can be expressed as:
- Total wages = (P's wage for 14 days) + (Q's wage for 24 days) + (R's wage for 20 days)
- Total wages = (2x * 14) + (3x * 24) + (5x * 20)

### Step 3: Substitute the values and set up the equation
Now substituting the values:
- Total wages = (28x) + (72x) + (100x) = 6000
- Combine like terms: 200x = 6000

### Step 4: Solve for x
To find the value of x, divide both sides by 200:
- x = 6000 / 200
- x = 30

### Step 5: Calculate individual wages for P, Q, and R
Now we can find the daily wages:
- P's daily wage = 2x = 2 * 30 = 60
- Q's daily wage = 3x = 3 * 30 = 90
- R's daily wage = 5x = 5 * 30 = 150

### Step 6: Calculate total wages for new working days
Now we need to find the total wages if:
- P works for 9 days
- Q works for 14 days
- R works for 8 days

Total wages can be calculated as:
- Total wages = (P's wage for 9 days) + (Q's wage for 14 days) + (R's wage for 8 days)
- Total wages = (60 * 9) + (90 * 14) + (150 * 8)

### Step 7: Substitute and calculate
Now substituting the values:
- Total wages = (540) + (1260) + (1200)

### Step 8: Add the total wages together
Now add them up:
- Total wages = 540 + 1260 + 1200 = 3000

### Final Answer
The total wages of P, Q, and R when P works for 9 days, Q for 14 days, and R for 8 days is Rs. 3000.

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