[tex]\(4 \, \text{kg}\)[/tex] of rice and [tex]\(3 \, \text{kg}\)[/tex] of wheat together cost Rs 145. If [tex]\(3 \, \text{kg}\)[/tex] of rice costs Rs 75, find the cost of [tex]\(4 \, \text{kg}\)[/tex] of wheat.
Certainly! Here’s the detailed, step-by-step solution to find the cost of 4 kg of wheat:
1. Determine the cost of 1 kg of rice: - We know that 3 kg of rice costs Rs 75. - To find the cost of 1 kg of rice, divide the total cost by the weight in kg. [tex]\[
\text{Cost of 1 kg of rice} = \frac{75 \text{ Rs}}{3 \text{ kg}} = 25 \text{ Rs/kg}
\][/tex]
2. Calculate the cost of 4 kg of rice: - Multiply the cost of 1 kg of rice by 4. [tex]\[
\text{Cost of 4 kg of rice} = 25 \text{ Rs/kg} \times 4 \text{ kg} = 100 \text{ Rs}
\][/tex]
3. Find the cost of 3 kg of wheat: - We are given that 4 kg of rice and 3 kg of wheat together cost Rs 145. - We already calculated the cost of 4 kg of rice to be Rs 100. - Subtract the cost of 4 kg of rice from the total cost to find the cost of 3 kg of wheat. [tex]\[
\text{Total cost} - \text{Cost of 4 kg of rice} = 145 \text{ Rs} - 100 \text{ Rs} = 45 \text{ Rs}
\][/tex]
4. Calculate the cost of 1 kg of wheat: - Divide the cost of 3 kg of wheat by 3 to find the cost of 1 kg of wheat. [tex]\[
\text{Cost of 1 kg of wheat} = \frac{45 \text{ Rs}}{3 \text{ kg}} = 15 \text{ Rs/kg}
\][/tex]
5. Determine the cost of 4 kg of wheat: - Multiply the cost of 1 kg of wheat by 4. [tex]\[
\text{Cost of 4 kg of wheat} = 15 \text{ Rs/kg} \times 4 \text{ kg} = 60 \text{ Rs}
\][/tex]
