Sure, let's solve the given problems step-by-step:
### Part a:
Problem:
If the cost of 1 kg of rice is Rs [tex]\(85 \frac{1}{2}\)[/tex], find the cost of 10 kg of rice.
Solution:
1. Convert the mixed fraction to an improper fraction:
Rs [tex]\(85 \frac{1}{2}\)[/tex] can be written as [tex]\(85 + \frac{1}{2}\)[/tex].
[tex]\[
85 + \frac{1}{2} = \frac{170}{2} + \frac{1}{2} = \frac{171}{2}
\][/tex]
2. Convert the improper fraction to a decimal, if necessary:
[tex]\[
\frac{171}{2} = 85.5
\][/tex]
3. Determine the cost of 10 kg of rice:
[tex]\[
\text{Cost per kg} = 85.5 \, \text{Rs}
\][/tex]
[tex]\[
\text{Total cost for 10 kg} = 85.5 \times 10 = 855 \, \text{Rs}
\][/tex]
Therefore, the cost of 10 kg of rice is Rs 855.
---
### Part b:
Problem:
A car can travel [tex]\(1\frac{3}{4}\)[/tex] km in 1 minute. How many kilometres does it travel in 12 minutes with the same speed?
Solution:
1. Convert the mixed fraction to an improper fraction:
[tex]\(1 \frac{3}{4}\)[/tex] can be written as [tex]\(1 + \frac{3}{4}\)[/tex].
[tex]\[
1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}
\][/tex]
2. Convert the improper fraction to a decimal, if necessary:
[tex]\[
\frac{7}{4} = 1.75
\][/tex]
3. Determine the distance traveled in 12 minutes:
[tex]\[
\text{Distance per minute} = 1.75 \, \text{km}
\][/tex]
[tex]\[
\text{Total distance in 12 minutes} = 1.75 \times 12 = 21 \, \text{km}
\][/tex]
Therefore, the car travels 21 kilometers in 12 minutes.
