The petrol tank of Vincent's bus was 70% empty. He went to the petrol station and topped up 37 ℓ of petrol. When he reached the hypermart, the petrol tank was 75% full. Given that he used 10 ℓ of fuel to get to the hypermart from the kiosk, find the capacity of the petrol tank.
| |
Full |
Empty |
Total |
| Before |
3x2 =
6 u |
7x2 =
14 u |
10x2 =
20 u |
| Change 1 |
+ 37 |
- 37 |
|
| Change 2 |
- 10 |
+ 10 |
|
| After |
3x5 =
15 u |
1x5 =
5 u |
4x5 =
20 u |
70% =
70100 =
710 Empty : Total = 7 : 10
75% =
75100 =
34 Full : Total = 3 : 4
The full capacity of the petrol tank is unchanged.
Make the totals the same. LCM of 10 and 4 is 20.
Volume of petrol in the end
= 6 u + 37 - 10
= 6 u + 27
15 u = 6 u + 27
15 u - 6 u = 27
9 u = 27
1 u = 27 ÷ 9 = 3
Capacity of the petrol tank
= 20 u
= 20 x 3
= 60 ℓ
Answer(s): 60 ℓ
