Answer :
To determine how many days it will take for Anjali and Banu to complete a job when working together, follow these steps:
1. Calculate each person's work rate:
Anjali can complete the job in 10 days, so her work rate is:
[tex]\[ \text{Anjali's work rate} = \frac{1 \, \text{job}}{10 \, \text{days}} = 0.1 \, \text{jobs per day} \][/tex]
Banu can complete the job in 5 days, so her work rate is:
[tex]\[ \text{Banu's work rate} = \frac{1 \, \text{job}}{5 \, \text{days}} = 0.2 \, \text{jobs per day} \][/tex]
2. Combine their work rates:
Working together, their combined work rate is the sum of their individual work rates:
[tex]\[ \text{Combined work rate} = \text{Anjali's work rate} + \text{Banu's work rate} = 0.1 + 0.2 = 0.3 \, \text{jobs per day} \][/tex]
3. Calculate the time to complete the job together:
The time \( T \) needed to complete one job at their combined work rate is:
[tex]\[ T = \frac{1 \, \text{job}}{\text{Combined work rate}} = \frac{1 \, \text{job}}{0.3 \, \text{jobs per day}} \approx 3.333 \, \text{days} \][/tex]
4. Convert decimal days to days and hours:
The integer part is the number of full days:
[tex]\[ \text{Full days} = 3 \, \text{days} \][/tex]
The fractional part represents the remaining time in hours:
[tex]\[ \text{Remaining time} = 0.333 \, \text{days} \times 24 \, \text{hours per day} \approx 8 \, \text{hours} \][/tex]
Therefore, if Anjali and Banu work together, they can complete the job in approximately 3 days and 8 hours.
Thus, the correct answer is:
(d) 3 days 8 hours [tex]$/ 3$[/tex] दिन 8 घंटे
1. Calculate each person's work rate:
Anjali can complete the job in 10 days, so her work rate is:
[tex]\[ \text{Anjali's work rate} = \frac{1 \, \text{job}}{10 \, \text{days}} = 0.1 \, \text{jobs per day} \][/tex]
Banu can complete the job in 5 days, so her work rate is:
[tex]\[ \text{Banu's work rate} = \frac{1 \, \text{job}}{5 \, \text{days}} = 0.2 \, \text{jobs per day} \][/tex]
2. Combine their work rates:
Working together, their combined work rate is the sum of their individual work rates:
[tex]\[ \text{Combined work rate} = \text{Anjali's work rate} + \text{Banu's work rate} = 0.1 + 0.2 = 0.3 \, \text{jobs per day} \][/tex]
3. Calculate the time to complete the job together:
The time \( T \) needed to complete one job at their combined work rate is:
[tex]\[ T = \frac{1 \, \text{job}}{\text{Combined work rate}} = \frac{1 \, \text{job}}{0.3 \, \text{jobs per day}} \approx 3.333 \, \text{days} \][/tex]
4. Convert decimal days to days and hours:
The integer part is the number of full days:
[tex]\[ \text{Full days} = 3 \, \text{days} \][/tex]
The fractional part represents the remaining time in hours:
[tex]\[ \text{Remaining time} = 0.333 \, \text{days} \times 24 \, \text{hours per day} \approx 8 \, \text{hours} \][/tex]
Therefore, if Anjali and Banu work together, they can complete the job in approximately 3 days and 8 hours.
Thus, the correct answer is:
(d) 3 days 8 hours [tex]$/ 3$[/tex] दिन 8 घंटे
