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
- 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?
- 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?
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?
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?
Important Questions from Work Efficiency
A and B together can complete a certain work in 20 days whereas B and C together can complete it in 24 days. If A is twice as good a workman as C, then in what time will B alone do 40% of the same work?
14 men can complete a work in 15 days. If 21 men are employed, then in how many days will they complete the same work?
A can do a certain work in 15 days, while B can do the same work in 21 days. If they work together, then in how many days will the same work be completed?
To do a certain work, A and B work on alternate days with B beginning the work on the first day. A alone can complete the same work in 24 days. If the work gets completed in \(11 \frac{1}{3}\) days, then B alone can complete \(\rm \frac{7}{9}^{th}\) part of the original work in:
Two men and 7 women can complete a work in 28 days whereas 6 men and 16 women can do the same work in 11 days. In how many days can 7 men complete the same work?
