Answer :
### Question 1
#### Problem:
If 12 labourers can earn [tex]\( \text{₹} 12,240 \)[/tex] in 12 days, how many labourers can earn [tex]\( \text{₹} 6,800 \)[/tex] in 8 days?
#### Solution:
1. Calculate the daily earning of one labourer:
- First, find the total earning per day for 12 labourers:
[tex]\[ \text{Daily total earning for 12 labourers} = \frac{12,240}{12 \text{ days}} = \text{₹} 1,020 \text{ per day} \][/tex]
- Then, find the daily earning for one labourer:
[tex]\[ \text{Daily earning per labourer} = \frac{\text{₹} 1,020}{12} = \text{₹} 85 \text{ per day} \][/tex]
2. Calculate the total earning for one labourer in 8 days:
[tex]\[ \text{Earning for one labourer in 8 days} = \text{₹} 85 \times 8 = \text{₹} 680 \][/tex]
3. Determine how many labourers are needed to earn ₹6,800 in 8 days:
- First, calculate the total amount 8 days of work represents for our unknown number of labourers:
[tex]\[ \text{Number of labourers} \times \text{₹} 680 = \text{₹} 6,800 \][/tex]
- Solving for the number of labourers:
[tex]\[ \text{Number of labourers} = \frac{₹ 6,800}{\text{₹} 680} = 10 \][/tex]
### Answer:
10 labourers can earn ₹6,800 in 8 days.
### Question 2
#### Problem:
If the wages of 4 men for 30 days amount to ₹3,900, find the wages of 20 men for 40 days.
#### Solution:
1. Calculate the daily wage for one man:
- First, find the total earning per day for 4 men:
[tex]\[ \text{Daily total earning for 4 men} = \frac{₹3,900}{30 \text{ days}} = ₹130 \text{ per day} \][/tex]
- Then, find the daily earning for one man:
[tex]\[ \text{Daily earning per man} = \frac{₹130}{4} = ₹32.50 \text{ per day} \][/tex]
2. Calculate the total wage for 20 men for 40 days:
[tex]\[ \text{Total earning for 20 men for 40 days} = 20 \text{ men} \times 40 \text{ days} \times ₹32.50 \text{ per day} \][/tex]
[tex]\[ \text{Total earning}= 20 \times 40 \times ₹32.50 = ₹26,000 \][/tex]
### Answer:
The wages of 20 men for 40 days amount to ₹26,000.
#### Problem:
If 12 labourers can earn [tex]\( \text{₹} 12,240 \)[/tex] in 12 days, how many labourers can earn [tex]\( \text{₹} 6,800 \)[/tex] in 8 days?
#### Solution:
1. Calculate the daily earning of one labourer:
- First, find the total earning per day for 12 labourers:
[tex]\[ \text{Daily total earning for 12 labourers} = \frac{12,240}{12 \text{ days}} = \text{₹} 1,020 \text{ per day} \][/tex]
- Then, find the daily earning for one labourer:
[tex]\[ \text{Daily earning per labourer} = \frac{\text{₹} 1,020}{12} = \text{₹} 85 \text{ per day} \][/tex]
2. Calculate the total earning for one labourer in 8 days:
[tex]\[ \text{Earning for one labourer in 8 days} = \text{₹} 85 \times 8 = \text{₹} 680 \][/tex]
3. Determine how many labourers are needed to earn ₹6,800 in 8 days:
- First, calculate the total amount 8 days of work represents for our unknown number of labourers:
[tex]\[ \text{Number of labourers} \times \text{₹} 680 = \text{₹} 6,800 \][/tex]
- Solving for the number of labourers:
[tex]\[ \text{Number of labourers} = \frac{₹ 6,800}{\text{₹} 680} = 10 \][/tex]
### Answer:
10 labourers can earn ₹6,800 in 8 days.
### Question 2
#### Problem:
If the wages of 4 men for 30 days amount to ₹3,900, find the wages of 20 men for 40 days.
#### Solution:
1. Calculate the daily wage for one man:
- First, find the total earning per day for 4 men:
[tex]\[ \text{Daily total earning for 4 men} = \frac{₹3,900}{30 \text{ days}} = ₹130 \text{ per day} \][/tex]
- Then, find the daily earning for one man:
[tex]\[ \text{Daily earning per man} = \frac{₹130}{4} = ₹32.50 \text{ per day} \][/tex]
2. Calculate the total wage for 20 men for 40 days:
[tex]\[ \text{Total earning for 20 men for 40 days} = 20 \text{ men} \times 40 \text{ days} \times ₹32.50 \text{ per day} \][/tex]
[tex]\[ \text{Total earning}= 20 \times 40 \times ₹32.50 = ₹26,000 \][/tex]
### Answer:
The wages of 20 men for 40 days amount to ₹26,000.
