Ram Lal is a renowned packager of fruits in Varanasi. He packs 70 mangoes or 56 guavas every day working 7 hours per day. His wife also helps him. She packs 30 mangoes or 24 guavas working 6 hours per day. Ram Lal has to pack 3300 mangoes and 2400 guavas with the help of his wife. They work alternatively, each day 10 hours. His wife started packaging on the first day and works on every alternate days. Similarly Ram Lal started his work on second day and worked alternatively till the completion of the work. In how many days the work will be finished?

Options

A. 85 days
B. `85(2)/(5)` days
C. 84 days
D. none of these

Answer

To solve the problem, we will first determine the packaging rates of Ram Lal and his wife for both mangoes and guavas. Then, we will calculate how much work they complete in a given time frame and finally find out how many days it will take to finish the work.

### Step 1: Calculate the packaging rates

**For Ram Lal:**
- He packs 70 mangoes in 7 hours.
- Therefore, his rate for mangoes = 70 mangoes / 7 hours = 10 mangoes per hour.
- He packs 56 guavas in 7 hours.
- Therefore, his rate for guavas = 56 guavas / 7 hours = 8 guavas per hour.

**For Ram Lal's wife:**
- She packs 30 mangoes in 6 hours.
- Therefore, her rate for mangoes = 30 mangoes / 6 hours = 5 mangoes per hour.
- She packs 24 guavas in 6 hours.
- Therefore, her rate for guavas = 24 guavas / 6 hours = 4 guavas per hour.

### Step 2: Calculate the total work required

- Total mangoes to pack = 3300
- Total guavas to pack = 2400

### Step 3: Calculate the work done in one complete cycle (2 days)

**Day 1 (Wife's turn):**
- She works for 10 hours.
- In 10 hours, she packs:
- Mangoes: 10 hours * 5 mangoes/hour = 50 mangoes
- Guavas: 10 hours * 4 guavas/hour = 40 guavas

**Day 2 (Ram Lal's turn):**
- He works for 10 hours.
- In 10 hours, he packs:
- Mangoes: 10 hours * 10 mangoes/hour = 100 mangoes
- Guavas: 10 hours * 8 guavas/hour = 80 guavas

**Total work done in 2 days:**
- Total mangoes packed in 2 days = 50 + 100 = 150 mangoes
- Total guavas packed in 2 days = 40 + 80 = 120 guavas

### Step 4: Calculate the number of cycles needed

**Total cycles needed for mangoes:**
- Total mangoes = 3300
- Work done in 2 days = 150
- Number of cycles = 3300 / 150 = 22 cycles

**Total cycles needed for guavas:**
- Total guavas = 2400
- Work done in 2 days = 120
- Number of cycles = 2400 / 120 = 20 cycles

### Step 5: Determine the limiting factor

The limiting factor is the number of cycles needed for guavas, which is 20 cycles. Each cycle takes 2 days.

### Step 6: Calculate total days required

- Total days = 20 cycles * 2 days/cycle = 40 days.

### Conclusion

The work will be finished in **40 days**.

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