If 30 men can complete a work in 40 days then in how many days 15 men will comple charge that porter charges to carry a bag of 50 kg of rice to a distance of 4 km is Rs 200 What is the charge to carry the bag of 30 kg of rice to a distance of 10 km ? 200 labourers need 50 days to construct a road of 4 km long. How many labourers are needed construct the 8 km long road in 80 days? If 30 men can do a piece of work in 11 days working 9 hours a day. For how many hours a de 55 men have to work in order to finish the work in 18 days?

Let's solve each of the problems step by step. ### Problem 1: Work Completion by Men If 30 men can complete a work in 40 days, we can find out how many days 15 men will take to complete the same work. 1. **Total Work**: \[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} = 30 \text{ men} \times 40 \text{ days} = 1200 \text{ man-days} \] 2. **Days for 15 Men**: \[ \text{Days} = \frac{\text{Total Work}}{\text{Number of Men}} = \frac{1200 \text{ man-days}}{15 \text{ men}} = 80 \text{ days} \] So, **15 men will take 80 days** to complete the work. ### Problem 2: Charge for Carrying Rice The porter charges Rs 200 to carry a 50 kg bag of rice for 4 km. We need to find the charge for a 30 kg bag for 10 km. 1. **Charge per kg per km**: \[ \text{Charge per kg for 4 km} = \frac{200 \text{ Rs}}{50 \text{ kg}} = 4 \text{ Rs/kg} \] \[ \text{Charge per kg per km} = \frac{4 \text{ Rs}}{4 \text{ km}} = 1 \text{ Rs/kg/km} \] 2. **Charge for 30 kg for 10 km**: \[ \text{Charge} = 30 \text{ kg} \times 10 \text{ km} \times 1 \text{ Rs/kg/km} = 300 \text{ Rs} \] So, the charge to carry the 30 kg bag of rice for 10 km is **Rs 300**. ### Problem 3: Labourers Needed for Road Construction 200 labourers can construct a 4 km long road in 50 days. We need to find out how many labourers are needed to construct an 8 km long road in 80 days. 1. **Total Work in Labour-days**: \[ \text{Total Work} = \text{Number of Labourers} \times \text{Number of Days} = 200 \text{ labourers} \times 50 \text{ days} = 10000 \text{ labour-days} \] 2. **Work Rate**: \[ \text{Work Rate} = \frac{10000 \text{ labour-days}}{4 \text{ km}} = 2500 \text{ labour-days/km} \] 3. **Total Work for 8 km**: \[ \text{Total Work for 8 km} = 2500 \text{ labour-days/km} \times 8 \text{ km} = 20000 \text{ labour-days} \] 4. **Labourers Needed for 80 Days**: \[ \text{Labourers} = \frac{\text{Total Work}}{\text{Number of Days}} = \frac{20000 \text{ labour-days}}{80 \text{ days}} = 250 \text{ labourers} \] So, **250 labourers are needed** to construct the 8 km long road in 80 days. ### Problem 4: Hours of Work for 55 Men If 30 men can do a piece of work in 11 days working 9 hours a day, we need to find out how many hours a day 55 men have to work to finish the work in 18 days. 1. **Total Work in Man-Hours**: \[ \text{Total Work} = \text{Number of Men} \times \text{Number of Days} \times \text{Hours per Day} = 30 \text{ men} \times 11 \text{ days} \times 9 \text{ hours/day} = 2970 \text{ man-hours} \] 2. **Hours per Day for 55 Men in 18 Days**: \[ \text{Hours per Day} = \frac{\text{Total Work}}{\text{Number of Men} \times \text{Number of Days}} = \frac{2970 \text{ man-hours}}{55 \text{ men} \times 18 \text{ days}} = \frac{2970}{990} = 3 \text{ hours/day} \] So, **55 men have to work 3 hours a day** to finish the work in 18 days.