Question

A car uses 10 litres of petrol in covering a distance of 145 km.
( i ) How many kilometres will it go in 20 litres of petrol ?
( ii ) How much petrol is required to cover a distance of 261 km?

Answer 1

Hint: In this question what we have to do is we are provided with the quantity of petrol and what we have to find how many kilometres will a car go in 20 litres of petrol and also how much petrol is required to cover a distance of 261 km. which we can calculate by concept of : we calculate petrol needed for per kilometre then we divide total number of kilometres by total petrol needed and when we calculate petrol needed for x km then we multiply x by petrol needed for per km.

Complete step by step answer:
Now, in question the only information which is provided is that A car is covering a distance of 145 km in 10 litres of petrol. And we have to find how many kilometres a car will go in 20 litres of petrol and also how much petrol is required to cover a distance of 261 km.
Now, let us first find how many kilometres does a car cover in 1 litre of petrol.
Here, the car covers 145 kilometres of distance in 10 litres.
So, in 10 litres = 145 km distance covered.
So, distance covered by a car in 1 litre of petrol will be equals to
1 litre $={\displaystyle \frac{145}{10}}$ km
 ${\displaystyle \frac{145}{10}}=14.5$km
That is, in one litre of petrol a car travels a total distance of 14.5 km.
Now, we have to find how many kilometres a car travels in 20 litres of petrol.
So, we have 1 litre $={\displaystyle \frac{145}{10}}$ km
Then, in 20 litre of petrol, we have
$$20\times 1litre$$ $={\displaystyle \frac{145}{10}}\times 20$ km
On Simplifying, we get
${\displaystyle \frac{145}{10}}\times 20=145\times 2km=290km.$
Hence in 20 litres of petrol a car travels a total distance of 290 km.
Now, we have to find that, to cover 261 kilometres how much litres of petrol do cars need.
If, we have 1 litre $={\displaystyle \frac{145}{10}}$ km, then
We can re - write it as ${\displaystyle \frac{10}{145}}litres=1km$ which means t cover 1 kilometre of distance, we need ${\displaystyle \frac{10}{145}}litres$ of petrol.
So, for 261 km of distance petrol needed will be equals to
$261\times 1km=261\times {\displaystyle \frac{10}{145}}litres$
On simplifying, we get
$261km={\displaystyle \frac{2610}{145}}litres$
Dividing 2610 by 145, we get
$261km=18litres$

So, to cover 261 kilometres, 18 litres of petrol is needed by a car.

Note: if it is given that in x litres of petrol, y km distance is covered by a car then ${\displaystyle \frac{y}{x}}$km/litre gives distance covered in 1 litre of petrol and ${\displaystyle \frac{x}{y}}$litre/km gives amount of petrol spent to cover distance of 1km. Calculation must be accurate and should be done carefully as we have to divide numbers of more than 2-digits. Always remember to place litres and km before the numerical answer to differentiate between litres and kilometres.