Pankaj can produce one unit in 15 days, while Bharti can do the same in 12 days. After producing one unit, working together, they received Rs. 90, which they distributed amongst themselves in proportional to their efficiency. If they work for 20 days, and sell the produce, then Bharti should receive

Options

A. Rs 120
B. Rs 140
C. Rs 150
D. Rs 160

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Determine the daily production rates of Pankaj and Bharti.
- Pankaj can produce 1 unit in 15 days, so his daily production rate is:
\[ \text{Pankaj's rate} = \frac{1}{15} \text{ units per day} \]
- Bharti can produce 1 unit in 12 days, so her daily production rate is:
\[ \text{Bharti's rate} = \frac{1}{12} \text{ units per day} \]

**Hint:** To find the daily production, divide 1 by the number of days taken to produce one unit.

### Step 2: Calculate their combined daily production rate.
- The combined production rate of Pankaj and Bharti is:
\[ \text{Combined rate} = \frac{1}{15} + \frac{1}{12} \]
- To add these fractions, find a common denominator (which is 60):
\[ \text{Combined rate} = \frac{4}{60} + \frac{5}{60} = \frac{9}{60} = \frac{3}{20} \text{ units per day} \]

**Hint:** When adding fractions, find a common denominator to combine them.

### Step 3: Calculate the total production in 20 days.
- In 20 days, the total production will be:
\[ \text{Total production} = \text{Combined rate} \times 20 = \frac{3}{20} \times 20 = 3 \text{ units} \]

**Hint:** Multiply the daily production rate by the number of days to find total production.

### Step 4: Calculate the total payment for the produced units.
- They receive Rs. 90 for 1 unit, so for 3 units, the total payment will be:
\[ \text{Total payment} = 3 \times 90 = 270 \text{ Rs.} \]

**Hint:** Multiply the payment for one unit by the total number of units produced.

### Step 5: Determine the ratio of their efficiencies.
- The efficiency ratio of Bharti to Pankaj is based on the time taken to produce one unit:
\[ \text{Efficiency ratio} = \frac{1/12}{1/15} = \frac{15}{12} = \frac{5}{4} \]

**Hint:** The efficiency ratio can be calculated by dividing the production rates.

### Step 6: Calculate the share of Bharti from the total payment.
- The total parts in the efficiency ratio (5 + 4 = 9) means:
- Bharti's share of the total payment is:
\[ \text{Bharti's share} = \frac{5}{9} \times 270 \]
- Calculate Bharti's share:
\[ \text{Bharti's share} = \frac{5 \times 270}{9} = \frac{1350}{9} = 150 \text{ Rs.} \]

**Hint:** To find an individual's share, multiply their part of the ratio by the total payment and divide by the total parts.

### Final Answer:
Bharti should receive **Rs. 150**.