The petrol tank of Tom's lorry was 80% empty. He went to the petrol kiosk and topped up 23 ℓ of petrol. When he reached the grocery store, the petrol tank was 90% full. Given that he used 9 ℓ of fuel to get to the grocery store 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 |
+ 23 |
- 23 |
|
Change 2 |
- 9 |
+ 9 |
|
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 + 23 - 9
= 2 u + 14
9 u = 2 u + 14
9 u - 2 u = 14
7 u = 14
1 u = 14 ÷ 7 = 2
Capacity of the petrol tank
= 10 u
= 10 x 2
= 20 ℓ
Answer(s): 20 ℓ