The petrol tank of Ken's lorry was 50% empty. He went to the petrol kiosk and topped up 12 ℓ of petrol. When he reached the bank, the petrol tank was 70% full. Given that he used 8 ℓ of fuel to get to the bank from the kiosk, find the capacity of the petrol tank.
|
Full |
Empty |
Total |
Before |
1x5 = 5 u |
1x5 = 5 u |
2x5 = 10 u |
Change 1 |
+ 12 |
- 12 |
|
Change 2 |
- 8 |
+ 8 |
|
After |
7x1 = 7 u |
3x1 = 3 u |
10x1 = 10 u |
50% =
50100 =
12 Empty : Total = 1 : 2
70% =
70100 =
710 Full : Total = 7 : 10
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 2 and 10 is 10.
Volume of petrol in the end
= 5 u + 12 - 8
= 5 u + 4
7 u = 5 u + 4
7 u - 5 u = 4
2 u = 4
1 u = 4 ÷ 2 = 2
Capacity of the petrol tank
= 10 u
= 10 x 2
= 20 ℓ
Answer(s): 20 ℓ