Work and Time: Calculating Amit's Painting Duration
This problem involves calculating the time taken by an individual based on relative efficiency compared to another person.
Understanding Efficiency and Time
Efficiency and the time taken to complete a task are inversely proportional. If someone is more efficient, they will take less time to finish the same job.
- Let the efficiency of Ajay be $E_A$.
- Let the efficiency of Amit be $E_M$.
- Let the time taken by Ajay be $T_A = 12$ days.
- Let the time taken by Amit be $T_M$.
Calculating Amit's Efficiency
Amit is 70% more efficient than Ajay. This means Amit's efficiency is Ajay's efficiency plus 70% of Ajay's efficiency.
Mathematically:
$E_M = E_A + (70\% \times E_A)$ $E_M = E_A + (0.70 \times E_A)$ $E_M = 1.70 \times E_A$Calculating Amit's Time
Since time is inversely proportional to efficiency ($T \propto \frac{1}{E}$), we can set up the ratio:
$\frac{T_M}{T_A} = \frac{E_A}{E_M}$Substitute the known values and the relationship between $E_M$ and $E_A$:
$\frac{T_M}{12 \text{ days}} = \frac{E_A}{1.70 \times E_A}$ $\frac{T_M}{12} = \frac{1}{1.70}$Now, solve for $T_M$:
$T_M = 12 \times \frac{1}{1.7}$ $T_M = \frac{12}{1.7}$To simplify, multiply the numerator and denominator by 10:
$T_M = \frac{120}{17}$Convert the improper fraction to a mixed number:
$120 \div 17 = 7$ with a remainder of $1$. $T_M = 7 \frac{1}{17}$ days.Conclusion
Amit would need $7 \frac{1}{17}$ days to finish the same painting.
Similar Questions
Three workers, X, Y, and Z, can complete a certain job in 10 days, 12 days, and 15 days, respectively. Determine the number of days required for them to complete the job when they work together.
If 5 workers, working at the same rate, complete a job in 12 days, how many days will 10 workers take to complete the same job?
- A piece of work can be done by 16 men in 8 days working 12 hours a day. How many men are needed to complete another work, which is three times the first one, in 24 days working 8 hours a day?
Important Questions from Time and work
In a circular race on a track of length 2000 m, X and Y start from the same point at the same time in opposite directions at the speeds of 15 km/h and 33 km/h, respectively. After how much time will they meet next?
Which of the following option figures will complete the pattern in the figure given below?
A has completed two-third of a job in 8 days, and B completes the rest of the job in 20 days. In how many days can they together complete the job?
The smallest 4-digit prime number is:
If Anand can do a piece of work in 9 days and Vinod can complete the same work in 6 days, then in how many days will both of them complete it together?
