Two friends Albert and Robert decide to buy a car. Albert pays `3/7` of the cost and Robert pays the rest.
(i) What fraction of the cost does Robert pay?
(ii) Robert pays Rs. 31540 more than Albert. Calculate the cost of the car.

Answer

Let's solve the problem step by step.

### Step 1: Determine the fraction of the cost that Robert pays.
Albert pays \( \frac{3}{7} \) of the cost of the car. To find out what fraction Robert pays, we can subtract Albert's fraction from the whole (which is represented as 1).

\[ \text{Fraction Robert pays} = 1 - \frac{3}{7} \]

### Step 2: Calculate Robert's fraction.
To perform the subtraction, we need to express 1 as a fraction with a denominator of 7.

\[ 1 = \frac{7}{7} \]

Now we can subtract:

\[ \text{Fraction Robert pays} = \frac{7}{7} - \frac{3}{7} = \frac{4}{7} \]

### Step 3: Write down the result for part (i).
So, Robert pays \( \frac{4}{7} \) of the cost of the car.

### Step 4: Set up the equation for part (ii).
Now, we know that Robert pays Rs. 31,540 more than Albert. Let's denote the total cost of the car as \( x \).

- Albert's payment: \( \frac{3}{7}x \)
- Robert's payment: \( \frac{4}{7}x \)

According to the problem, we can set up the following equation:

\[ \frac{4}{7}x - \frac{3}{7}x = 31,540 \]

### Step 5: Simplify the equation.
Subtract the fractions:

\[ \frac{4x - 3x}{7} = 31,540 \]

This simplifies to:

\[ \frac{x}{7} = 31,540 \]

### Step 6: Solve for \( x \).
To find \( x \), multiply both sides of the equation by 7:

\[ x = 31,540 \times 7 \]

### Step 7: Calculate the total cost.
Now we perform the multiplication:

\[ x = 31,540 \times 7 = 220,780 \]

### Step 8: Write down the final answer for part (ii).
The total cost of the car is Rs. 220,780.

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