IDNLearn.com is your go-to resource for finding answers to any question you have. Discover in-depth and reliable answers to all your questions from our knowledgeable community members who are always ready to assist.

Oilibya filling station in Machakos makes a profit of Ksh. 520 for every 1000 litres of petrol sold and Ksh. 480 for every 1000 litres of diesel sold. In a certain month, the dealer sold twice as much diesel as petrol. If the total fuel sold that month was 900,000 litres, find the dealer's profit for the month.

(4 marks)


Sagot :

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.
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.