Certainly! Let's solve the problem step-by-step.
### Step 1: Define the Variables
Let's denote:
- [tex]\( a \)[/tex] as the cost of 1 kg of apples (in Rs)
- [tex]\( o \)[/tex] as the cost of 1 kg of oranges (in Rs)
### Step 2: Formulate the Equations
Based on the problem, we can extract two key pieces of information leading to two equations:
1. The total cost of 4 kg of apples and 6 kg of oranges is Rs 1,540.
[tex]\[
4a + 6o = 1540
\][/tex]
2. The cost of 1 kg of apples is the same as the cost of 2 kg of oranges.
[tex]\[
a = 2o
\][/tex]
### Step 3: Substitute and Solve
We can substitute the second equation into the first one.
Since [tex]\( a = 2o \)[/tex], substitute [tex]\( 2o \)[/tex] for [tex]\( a \)[/tex] in the first equation:
[tex]\[
4(2o) + 6o = 1540
\][/tex]
This simplifies to:
[tex]\[
8o + 6o = 1540
\][/tex]
[tex]\[
14o = 1540
\][/tex]
Now solve for [tex]\( o \)[/tex]:
[tex]\[
o = \frac{1540}{14}
\][/tex]
[tex]\[
o = 110
\][/tex]
So, the cost of 1 kg of oranges is [tex]\( Rs 110 \)[/tex].
### Step 4: Find the Cost of Apples
Using the relationship [tex]\( a = 2o \)[/tex]:
[tex]\[
a = 2 \times 110
\][/tex]
[tex]\[
a = 220
\][/tex]
So, the cost of 1 kg of apples is [tex]\( Rs 220 \)[/tex].
### Summary
- The cost of 1 kg of apples is Rs 220.
- The cost of 1 kg of oranges is Rs 110.
