8. If the cost of [tex]\(5 \frac{1}{2} \text{ kg}\)[/tex] of sugar is [tex]\(₹ 206 \frac{1}{4}\)[/tex], then find the cost of [tex]\(8 \frac{1}{4} \text{ kg}\)[/tex] of sugar.



Answer :

Sure, let's solve this step-by-step.

1. Understanding the Given Values:
- The cost of [tex]\(5 \frac{1}{2} \, \text{kg}\)[/tex] of sugar is [tex]\( ₹ 206 \frac{1}{4} \)[/tex].
- This can be written as:
[tex]\[ 5 \frac{1}{2} \, \text{kg} = 5.5 \, \text{kg} \][/tex]
[tex]\[ ₹ 206 \frac{1}{4} = ₹ 206.25 \][/tex]

2. Finding the Cost per Kilogram:
- To find the cost per kilogram, we divide the total cost by the total weight.
[tex]\[ \text{Cost per kilogram} = \frac{₹ 206.25}{5.5 \, \text{kg}} \][/tex]

3. Calculate the Cost per Kilogram:
[tex]\[ \text{Cost per kilogram} = ₹ 37.5 \][/tex]

4. Finding the Total Cost for [tex]\(8 \frac{1}{4} \, \text{kg}\)[/tex]:
- Next, we need to find the cost for [tex]\(8 \frac{1}{4} \, \text{kg}\)[/tex]. This can be written as:
[tex]\[ 8 \frac{1}{4} \, \text{kg} = 8.25 \, \text{kg} \][/tex]

- Using the cost per kilogram calculated above, we find:
[tex]\[ \text{Total cost of } 8.25 \, \text{kg} = ₹ 37.5 \times 8.25 \, \text{kg} \][/tex]

5. Calculate the Total Cost:
[tex]\[ \text{Total cost} = ₹ 309.375 \][/tex]

So, the cost of [tex]\(8 \frac{1}{4} \, \text{kg}\)[/tex] of sugar is [tex]\(₹ 309.375\)[/tex].