Calculating Ajay's Work Completion Time
This solution explains how to find the number of days Ajay needs to complete a work, given Sameer's time and Ajay's increased efficiency.
Understanding Work Rate
The rate of work is the amount of work done per unit of time. If Sameer completes a work in 16 days, we can represent his rate.
- Let the total work be $W$.
- Let Sameer's time be $T_S = 16$ days.
- Sameer's work rate is $R_S = \frac{W}{T_S} = \frac{W}{16}$ units of work per day.
Ajay's Efficiency and Rate
Ajay's efficiency is 60% more than Sameer's. This means Ajay works faster.
- Ajay's efficiency = Sameer's efficiency + 60% of Sameer's efficiency.
- Ajay's rate, $R_A = R_S + (0.60 \times R_S) = 1.60 \times R_S$.
- Substituting Sameer's rate: $R_A = 1.60 \times \frac{W}{16}$.
Ajay's Time Calculation
The time taken to complete the work is inversely proportional to the work rate. We need to find the time Ajay takes ($T_A$).
- Formula: $T_A = \frac{W}{R_A}$.
- Substitute the expression for $R_A$: $T_A = \frac{W}{1.60 \times \frac{W}{16}}$.
- Simplify the expression: $T_A = \frac{W \times 16}{1.60 \times W}$.
- Cancel out $W$: $T_A = \frac{16}{1.60}$.
- Calculate the final value: $T_A = \frac{16}{16/10} = 16 \times \frac{10}{16} = 10$ days.
Therefore, Ajay will complete the work in 10 days.
Similar Questions
- A can complete a task in $30\text{ days}$, and B can complete the same task in $40\text{ days}$. They work together for $10\text{ days}$, and then C joins them and completes the remaining work in $5\text{ days}$. How long will C alone take to complete the task?
A and B can complete a task in 12 days together. A is 25% more efficient than B. What percentage of the work is done by A alone?
- The efficiency of A, B and C is 2 : 3 : 5. A alone can complete the work in 40 days. They all worked together for 5 days and then C left the work. In how many days can A and B together complete the remaining work?
20 women can do work in 16 days. 10 men can complete the same work in 12 days. What is the ratio between the efficiency of a man and a woman?
Important Questions from Work Efficiency
A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work further increased by 50%?
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
A and B together can do a piece of work in 4 days, B and C can do it in 6 days, A and C can do it in 8 days. Then A, B and C together can do the same work in :-
A can complete 50% of a work in 9 days and B can do 25% of the work in 9 days, if they work alone. If they work together then how much work (in percentage) can be completed in 6 days?
A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for A alone to paint the house?
