Calculating Men and Women Earnings Over Time
This problem involves calculating the daily earnings of men and women based on group earnings and then determining the time required for individuals to earn a specific amount.
Setting Up Earnings Equations
Let the daily earning of one man be denoted by \(m\) and the daily earning of one woman be denoted by \(w\).
- From the first statement: 2 men and 3 women earn ₹49 in 7 days. This translates to the equation: \( (2m + 3w) \times 7 = 49 \) Simplifying, we get: \( 2m + 3w = \frac{49}{7} \) So, \( 2m + 3w = 7 \) (Equation 1)
- From the second statement: 3 men and 6 women earn ₹96 in 8 days. This translates to the equation: \( (3m + 6w) \times 8 = 96 \) Simplifying, we get: \( 3m + 6w = \frac{96}{8} \) So, \( 3m + 6w = 12 \). Dividing by 3, we get \( m + 2w = 4 \) (Equation 2)
Solving for Individual Daily Earnings
We need to solve the system of linear equations formed by Equation 1 and Equation 2.
- From Equation 2, express \(m\) in terms of \(w\): \( m = 4 - 2w \)
- Substitute this expression for \(m\) into Equation 1: \( 2(4 - 2w) + 3w = 7 \) \( 8 - 4w + 3w = 7 \) \( 8 - w = 7 \) \( w = 8 - 7 \) \( w = 1 \)
- Substitute the value of \(w\) back into the expression for \(m\): \( m = 4 - 2(1) \) \( m = 4 - 2 \) \( m = 2 \)
Therefore, one man earns ₹2 per day, and one woman earns ₹1 per day.
Calculating Time for ₹27 Earnings
We need to find the time it takes for 1 man and 1 woman to earn ₹27.
- Calculate the combined daily earning of 1 man and 1 woman: Combined Earning = \( m + w = 2 + 1 = 3 \) rupees per day.
- Calculate the time required to earn ₹27: Time = Total Amount / Daily Earning Rate Time = \( \frac{27}{3} \) Time = 9 days
It will take 9 days for 1 man and 1 woman to earn ₹27.
Similar Questions
If the wages for 9 workers for 8 days are ₹2,880, what will be the wages for 15 workers for 9 days at the same rate?
- 12 skilled, 14 semi-killed and 10 unskilled workers complete a job for ₹13189. If their individual wages be in the ratio of 9:5:4, then the total money (in ₹) earned by 10 unskilled workers is:
- A alone can finish a job in 12 days, while B alone can finish it in 15 days. With the help of C, they can finish the same job in 5 days. If they are paid ₹2,880 for the whole job, what will be the share of C?
- X, Y and Z together earn ₹2,400/- in 15 days. X and Y together earn ₹1,840/- in 16 days. Y and Z together earn ₹1,530/- in 18 days. What is the daily earning (in ₹) of Y?
- Ram and Shyam can complete a work in 12 and 18 days respectively. They worked together and received ₹15,000 for doing the work. How much money did they receive individually?
- A alone can finish a task in 20 days, while B alone can finish it in 15 days. They together work for 5 days and stop, then the rest of the work is finished by C alone in 2 days. If they get paid ₹2,400 for finishing the whole task, then find the difference between the daily wages of C and A.
Important Questions from Work and Wages
A can complete a work alone in 8 days. B can complete the same work alone in 12 days. C alone complete the same work in 16 days. They complete the work in 3 days with the help of D. If they get Rs.12000 for the work, then how much money does the D get?
If 15 men can complete a work in 16 days by working 8 hours daily, then in how many days will 10 men complete the work by working 12 hours daily?
10 men working 8 hours a day can finish a work in 28 days. In how many days, 8 men working 5 hours a day with complete 50% of that work?
Twenty lamps can be lighted for 6 hr a day for 20 days at a cost of Rs. 100. How much would be the cost of lighting 40 lamps, 8 hr for 12 days?
Six men can complete a job in two days. Four boys can complete the same job in eight days. In how many days would three men and six boys, working together, be able to complete the job?
