The petrol tank of Paul's van was 75% empty. He went to the petrol station and topped up 27 ℓ of petrol. When he reached the park, the petrol tank was 90% full. Given that he used 1 ℓ of fuel to get to the park from the kiosk, find the capacity of the petrol tank.
|
Full |
Empty |
Total |
Before |
1x5 = 5 u |
3x5 = 15 u |
4x5 = 20 u |
Change 1 |
+ 27 |
- 27 |
|
Change 2 |
- 1 |
+ 1 |
|
After |
9x2 = 18 u |
1x2 = 2 u |
10x2 = 20 u |
75% =
75100 =
34 Empty : Total = 3 : 4
90% =
90100 =
910 Full : Total = 9 : 10
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 4 and 10 is 20.
Volume of petrol in the end
= 5 u + 27 - 1
= 5 u + 26
18 u = 5 u + 26
18 u - 5 u = 26
13 u = 26
1 u = 26 ÷ 13 = 2
Capacity of the petrol tank
= 20 u
= 20 x 2
= 40 ℓ
Answer(s): 40 ℓ