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breadth, find the length and the breadth of the field.
eative section - A
a) The total cost of 4 kg of apples and 6 of oranges is Rs 1,540. If the cost of 1 kg of
apples is the same as
the cost of 2 kg of oranges, find the rate of cost of apples and
oranges.



Answer :

GinnyAnswer
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.

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