The petrol tank of Vincent's van was 75% empty. He went to the petrol station and topped up 36 ℓ of petrol. When he reached the hospital, the petrol tank was 90% full. Given that he used 10 ℓ of fuel to get to the hospital 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 |
+ 36 |
- 36 |
|
| Change 2 |
- 10 |
+ 10 |
|
| 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 + 36 - 10
= 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
