Work and Wages Calculation
The problem involves calculating individual earnings based on work completion time when working together.
Understanding Work Rates
- Manish completes the work in 7 days. His daily work rate is $\frac{1}{7}$.
- Anil completes the work in 6 days. His daily work rate is $\frac{1}{6}$.
Ratio of Work Done
When they work together, their earnings are proportional to the amount of work they contribute. The ratio of work done is the inverse ratio of the time taken.
- Ratio of time taken (Manish : Anil) = 7 : 6
- Ratio of work done (Manish : Anil) = $\frac{1}{7} : \frac{1}{6}$
- To simplify, multiply by the LCM of 7 and 6 (which is 42):
- Ratio of earnings = $(\frac{1}{7} \times 42) : (\frac{1}{6} \times 42)$ = 6 : 7
Calculating Manish's Earnings
The total wage is Rs. 390. The earnings are distributed according to the ratio 6 : 7.
- Total parts in the ratio = 6 + 7 = 13 parts.
- Manish's share is 6 parts out of 13.
- Manish's earnings = $\frac{\text{Manish's ratio part}}{\text{Total ratio parts}} \times \text{Total Wage}$
- Manish's earnings = $\frac{6}{13} \times 390$
- Manish's earnings = $6 \times \frac{390}{13}$
- Manish's earnings = $6 \times 30$
- Manish's earnings = Rs. 180
Important Questions from Work and Wages
A and B worked together and received a total of Rs. 18,000 for 15 days. A's efficiency in the work was 5 times that of B's. The daily wage of A (in Rs.) was:
Samir and Puneet can complete the same work in 10 days and 15 days respectively. The work was assigned for Rs.4500. After working together for 3 days Samir and Puneet involved Ashok. The work was completed in total 5 days. What amount (in Rs.) was paid to Ashok?
5 women and 9 girls earn a total of ₹18,720 in 9 days, while 9 women and 16 girls earn a total of ₹ 52,080 in 14 days. How much will 12 women and 7 girls together earn (in ₹) in 13 days?
X, Y and Z completed a work costing Rs. 3,400, X worked for 5 days, Y for 7 days and Z for 10 days. If their daily wages are in the ratio of 4 ∶ 5 ∶ 3, how much amount will be received by X?
A,B and C can do a work in 10 days, 15 days, and 20 days, respectively. They finished that work together and got Rs. 2,600 as wages. Find C's wage.
