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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.

Verified Answer :

GinnyAnswer

Certainly! Let's solve the problem step-by-step.

### Step 1: Define the Variables
Let's denote:
- \(\( a \)\) as the cost of 1 kg of apples (in Rs)
- \(\( o \)\) 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.
\(\[ 4a + 6o = 1540 \]\)

2. The cost of 1 kg of apples is the same as the cost of 2 kg of oranges.
\(\[ a = 2o \]\)

### Step 3: Substitute and Solve
We can substitute the second equation into the first one.

Since \(\( a = 2o \)\), substitute \(\( 2o \)\) for \(\( a \)\) in the first equation:
\(\[ 4(2o) + 6o = 1540 \]\)

This simplifies to:
\(\[ 8o + 6o = 1540 \]\)
\(\[ 14o = 1540 \]\)

Now solve for \(\( o \)\):
\(\[ o = \frac{1540}{14} \]\)
\(\[ o = 110 \]\)

So, the cost of 1 kg of oranges is \(\( Rs 110 \)\).

### Step 4: Find the Cost of Apples
Using the relationship \(\( a = 2o \)\):
\(\[ a = 2 \times 110 \]\)
\(\[ a = 220 \]\)

So, the cost of 1 kg of apples is \(\( Rs 220 \)\).

### 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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