Answer :
Sure! Let's solve each part of the exercise step by step:
1. If 12 kg of rice costs 696, find the cost of 17 kg of rice.
- First, find the cost per kg of rice:
[tex]\[
\text{Cost per kg} = \frac{696}{12} = 58 \text{ units}
\][/tex]
- Now, to find the cost of 17 kg:
[tex]\[
\text{Cost of 17 kg} = 17 \times 58 = 986 \text{ units}
\][/tex]
2. If 750 g of milk provides 24.75 g of protein, how many grams of protein does 100 g of milk provide?
- Find the protein provided per gram of milk:
[tex]\[
\text{Protein per gram} = \frac{24.75}{750} = 0.033 \text{ g}
\][/tex]
- Then, calculate the protein in 100 g of milk:
[tex]\[
\text{Protein in 100 g} = 100 \times 0.033 = 3.3 \text{ g}
\][/tex]
3. A dozen mangoes weigh 4.8 kg. How many mangoes will weigh 11.2 kg?
- Find how many mangoes correspond to 1 kg:
[tex]\[
\text{Mangoes per kg} = \frac{12}{4.8} = 2.5 \text{ mangoes/kg}
\][/tex]
- Calculate how many mangoes weigh 11.2 kg:
[tex]\[
\text{Mangoes in 11.2 kg} = 11.2 \times 2.5 = 28 \text{ mangoes}
\][/tex]
4. A car can cover a distance of 330 km on 25 litres of petrol. How far can it travel on 17 litres of petrol?
- First, determine how many kilometers can be covered per litre:
[tex]\[
\text{Distance per litre} = \frac{330}{25} = 13.2 \text{ km/litre}
\][/tex]
- Now find the distance for 17 litres:
[tex]\[
\text{Distance for 17 litres} = 17 \times 13.2 = 224.4 \text{ km}
\][/tex]
5. A pipe can fill 4 water tanks in 2 h 20 min. How long will it take to fill 7 such tanks?
- Convert 2 h 20 min to hours:
[tex]\[
\text{Time in hours} = 2 + \frac{20}{60} = 2.333 \text{ hours}
\][/tex]
- Find the time to fill one tank:
[tex]\[
\text{Time for 1 tank} = \frac{2.333}{4} = 0.5833 \text{ hours}
\][/tex]
- Calculate the time for 7 tanks:
[tex]\[
\text{Time for 7 tanks} = 7 \times 0.5833 = 4.0833 \text{ hours}
\][/tex]
6. If 54 men can finish a piece of work in 49 days, how many men are needed to finish it in 42 days?
- First, find the total work in man-days:
[tex]\[
\text{Total work} = 54 \times 49 = 2646 \text{ man-days}
\][/tex]
- Find the number of men needed for 42 days:
[tex]\[
\text{Men needed} = \frac{2646}{42} = 63 \text{ men}
\][/tex]
7. If 12 men can reap a field in 8 days, how many days can 16 men reap the same field?
- Calculate the total work units in man-days:
[tex]\[
\text{Total work} = 12 \times 8 = 96 \text{ man-days}
\][/tex]
- Find the number of days for 16 men:
[tex]\[
\text{Days for 16 men} = \frac{96}{16} = 6 \text{ days}
\][/tex]
These calculations yield a complete and verified solution to each part of the exercise!
1. If 12 kg of rice costs 696, find the cost of 17 kg of rice.
- First, find the cost per kg of rice:
[tex]\[
\text{Cost per kg} = \frac{696}{12} = 58 \text{ units}
\][/tex]
- Now, to find the cost of 17 kg:
[tex]\[
\text{Cost of 17 kg} = 17 \times 58 = 986 \text{ units}
\][/tex]
2. If 750 g of milk provides 24.75 g of protein, how many grams of protein does 100 g of milk provide?
- Find the protein provided per gram of milk:
[tex]\[
\text{Protein per gram} = \frac{24.75}{750} = 0.033 \text{ g}
\][/tex]
- Then, calculate the protein in 100 g of milk:
[tex]\[
\text{Protein in 100 g} = 100 \times 0.033 = 3.3 \text{ g}
\][/tex]
3. A dozen mangoes weigh 4.8 kg. How many mangoes will weigh 11.2 kg?
- Find how many mangoes correspond to 1 kg:
[tex]\[
\text{Mangoes per kg} = \frac{12}{4.8} = 2.5 \text{ mangoes/kg}
\][/tex]
- Calculate how many mangoes weigh 11.2 kg:
[tex]\[
\text{Mangoes in 11.2 kg} = 11.2 \times 2.5 = 28 \text{ mangoes}
\][/tex]
4. A car can cover a distance of 330 km on 25 litres of petrol. How far can it travel on 17 litres of petrol?
- First, determine how many kilometers can be covered per litre:
[tex]\[
\text{Distance per litre} = \frac{330}{25} = 13.2 \text{ km/litre}
\][/tex]
- Now find the distance for 17 litres:
[tex]\[
\text{Distance for 17 litres} = 17 \times 13.2 = 224.4 \text{ km}
\][/tex]
5. A pipe can fill 4 water tanks in 2 h 20 min. How long will it take to fill 7 such tanks?
- Convert 2 h 20 min to hours:
[tex]\[
\text{Time in hours} = 2 + \frac{20}{60} = 2.333 \text{ hours}
\][/tex]
- Find the time to fill one tank:
[tex]\[
\text{Time for 1 tank} = \frac{2.333}{4} = 0.5833 \text{ hours}
\][/tex]
- Calculate the time for 7 tanks:
[tex]\[
\text{Time for 7 tanks} = 7 \times 0.5833 = 4.0833 \text{ hours}
\][/tex]
6. If 54 men can finish a piece of work in 49 days, how many men are needed to finish it in 42 days?
- First, find the total work in man-days:
[tex]\[
\text{Total work} = 54 \times 49 = 2646 \text{ man-days}
\][/tex]
- Find the number of men needed for 42 days:
[tex]\[
\text{Men needed} = \frac{2646}{42} = 63 \text{ men}
\][/tex]
7. If 12 men can reap a field in 8 days, how many days can 16 men reap the same field?
- Calculate the total work units in man-days:
[tex]\[
\text{Total work} = 12 \times 8 = 96 \text{ man-days}
\][/tex]
- Find the number of days for 16 men:
[tex]\[
\text{Days for 16 men} = \frac{96}{16} = 6 \text{ days}
\][/tex]
These calculations yield a complete and verified solution to each part of the exercise!
