The petrol tank of Xavier's van was 80% empty. He went to the petrol station and topped up 45 ℓ of petrol. When he reached the hypermart, the petrol tank was 90% full. Given that he used 3 ℓ of fuel to get to the hypermart from the kiosk, find the capacity of the petrol tank.
| |
Full |
Empty |
Total |
| Before |
1x2 =
2 u |
4x2 =
8 u |
5x2 =
10 u |
| Change 1 |
+ 45 |
- 45 |
|
| Change 2 |
- 3 |
+ 3 |
|
| After |
9x1 =
9 u |
1x1 =
1 u |
10x1 =
10 u |
80% =
80100 =
45 Empty : Total = 4 : 5
90% =
90100 =
910 Full : Total = 9 : 10
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 5 and 10 is 10.
Volume of petrol in the end
= 2 u + 45 - 3
= 2 u + 42
9 u = 2 u + 42
9 u - 2 u = 42
7 u = 42
1 u = 42 ÷ 7 = 6
Capacity of the petrol tank
= 10 u
= 10 x 6
= 60 ℓ
Answer(s): 60 ℓ
