₹$7560$
This problem involves calculating the combined daily earnings of a group consisting of both men and women, given their individual earning capacities over a specific period.
Determining Men and Women Earning Rates
The problem states that $6$ men or $5$ women earn a total of ₹ $16,800$ in $4$ days. First, let's find out how much is earned per day.
Total earnings = ₹ $16,800$
Number of days = $4$
Daily earnings = Total earnings / Number of days
Using LaTeX: Daily earnings = $\frac{16,800}{4} = ₹ 4,200$
This means that the combined earning power of $6$ men in one day is ₹ $4,200$, and similarly, the combined earning power of $5$ women in one day is also ₹ $4,200$.
Calculating Individual Daily Earnings
Now, we can find the daily earning rate for one man and one woman.
Earning rate for men:
$6$ men earn ₹ $4,200$ in $1$ day.
Earning per man per day = Daily earnings of 6 men / 6
Using LaTeX: Earning per man per day = $\frac{4,200}{6} = ₹ 700$
Earning rate for women:
$5$ women earn ₹ $4,200$ in $1$ day.
Earning per woman per day = Daily earnings of 5 women / 5
Using LaTeX: Earning per woman per day = $\frac{4,200}{5} = ₹ 840$
Calculating Combined Earnings for the New Group
We need to find how much $4$ women and $6$ men will earn in one day.
Earnings of 4 women in 1 day:
Earnings = Number of women × Earning per woman per day
Using LaTeX: Earnings = $4 \times 700 = ₹ 3,360$
Correction: Earning per woman per day is ₹840.
Using LaTeX: Earnings = $4 \times 840 = ₹ 3,360$
Earnings of 6 men in 1 day:
Earnings = Number of men × Earning per man per day
Using LaTeX: Earnings = $6 \times 700 = ₹ 4,200$
Total combined earnings in 1 day:
Total earnings = Earnings of 4 women + Earnings of 6 men
Using LaTeX: Total earnings = $3,360 + 4,200 = ₹ 7,560$
Therefore, $4$ women and $6$ men will earn ₹ $7,560$ in one day.
Important Questions from Time & Work (Notes)
- If 6 men and 8 boys can do a piece of work in 10 days and 26 men and 48 boys can do the same work in 2 days, then the time taken by 15 men and 20 boys to do the same work will be
- A fresh water tap fills a fish tank in 40 minutes. The same tank is filled by a salt water tap in 120 minutes. If both the taps are open, how many minutes will it take to fill the tank?
Three pipes A, B and C can fill a tank in $10$, $15$ and $20$ hours respectively. Pipe A was opened at $6$ AM, pipe B at $7$ AM and pipe C at $8$ AM. At what time was the tank completely filled, if pipe C needs a break of $1$ hour after remaining open for $3$ hours?
A tank has four pipes $P_1$, $P_2$, $P_3$ and $P_4$. The tank can be filled in $15$ minutes by pipes $P_1$, $P_2$, $P_3$ together. It can be filled in $20$ minutes by pipes $P_2$, $P_3$, $P_4$ together and it can be filled by pipes $P_1$, $P_4$ together in $30$ minutes. If all the pipes are opened together, then in how much time will the tank be filled?
$5$ men and $4$ women can earn ₹ $20000$ in $8$ days. $10$ men and $7$ women can earn ₹ $23,750$ in $5$ days. In how many days will $5$ men and $6$ women earn ₹ $12,000$?
