To find the dealer's profit for the month, we can solve the problem step-by-step based on the given data and conditions. Here are the steps:
1. Identify the given data:
- Profit for every 1000 litres of petrol sold: Ksh. 520
- Profit for every 1000 litres of diesel sold: Ksh. 480
- Total fuel sold: 900,000 litres
- Diesel sold is twice the amount of petrol sold.
2. Determine the amount of petrol and diesel sold:
- Let [tex]\( x \)[/tex] be the amount of petrol sold in litres.
- Therefore, the amount of diesel sold is [tex]\( 2x \)[/tex] litres (since diesel sold is twice the amount of petrol).
- The total amount of fuel sold is [tex]\( x + 2x = 3x \)[/tex].
Given that the total fuel sold is 900,000 litres, we can set up the equation:
[tex]\[ 3x = 900,000 \][/tex]
Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{900,000}{3} = 300,000 \][/tex]
Thus, the amount of petrol sold is 300,000 litres.
3. Calculate the amount of diesel sold:
Since the diesel sold is twice the amount of petrol sold:
[tex]\[ \text{Diesel sold} = 2 \times 300,000 = 600,000 \text{ litres} \][/tex]
4. Calculate the total profit from petrol and diesel:
- Total profit from petrol:
[tex]\[ \text{Total profit from petrol} = \left( \frac{300,000}{1000} \right) \times 520 = 300 \times 520 = 156,000 \text{ Ksh} \][/tex]
- Total profit from diesel:
[tex]\[ \text{Total profit from diesel} = \left( \frac{600,000}{1000} \right) \times 480 = 600 \times 480 = 288,000 \text{ Ksh} \][/tex]
5. Calculate the dealer's total profit for the month:
Adding the profits from petrol and diesel:
[tex]\[ \text{Total profit} = 156,000 \text{ Ksh} + 288,000 \text{ Ksh} = 444,000 \text{ Ksh} \][/tex]
Therefore, the dealer's total profit for the month is Ksh. 444,000.
