The petrol tank of Howard's van was 80% empty. He went to the petrol kiosk and topped up 32 ℓ of petrol. When he reached the cinema, the petrol tank was 95% full. Given that he used 2 ℓ of fuel to get to the cinema from the kiosk, find the capacity of the petrol tank.
| |
Full |
Empty |
Total |
| Before |
1x4 =
4 u |
4x4 =
16 u |
5x4 =
20 u |
| Change 1 |
+ 32 |
- 32 |
|
| Change 2 |
- 2 |
+ 2 |
|
| After |
19x1 =
19 u |
1x1 =
1 u |
20x1 =
20 u |
80% =
80100 =
45 Empty : Total = 4 : 5
95% =
95100 =
1920 Full : Total = 19 : 20
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 5 and 20 is 20.
Volume of petrol in the end
= 4 u + 32 - 2
= 4 u + 30
19 u = 4 u + 30
19 u - 4 u = 30
15 u = 30
1 u = 30 ÷ 15 = 2
Capacity of the petrol tank
= 20 u
= 20 x 2
= 40 ℓ
Answer(s): 40 ℓ
