Question

A 60-litre tank was full of oil. Sam used 40% of it and poured the rest into a 40-litre tank.
1) What percent of the 40-litre tank was filled with oil?
2) If Sam used 3-litres of oil daily, what percent of the oil in the 40-litres tank would be used in 10 days?

Answer 1

Hint:
A 60-litre tank was full of oil means that there is 60-litre of oil. First calculate 40% of 60-litre to obtain the amount of oil used by Sam. To calculate the amount of oil remaining subtract the used amount of oil from 60-litres. Let this be \[x\]. Now you need to calculate what percentage of 40 is \[x\]. Sam used 3-litres of oil from \[x\] daily. So in 10 days Sam will use \[y = 3 \times 10\] litres. Now calculate what percent of \[x\] is \[y\].

Complete step by step solution:
Given:
Amount of oil originally= 60L
Amount of oil used by Sam=\[40\%\text{ of }60L\]
The remaining oil is filled in a 40L tank.
And Sam uses 3L oil daily for 10 days from this tank.
A 60L tank is full of oil implies that amount of oil= 60L
Sam uses 40% of the oil.
Amount of oil Sam uses\[ = \dfrac{{40}}{{100}} \times 60 = 24L\]
Amount of oil remaining
\[ = \left( {60 - 24} \right)L\]
\[ = 36L\]
In (i), 36L of oil is poured into a 40L tank.
To calculate what per unit of this tank is filled.
Assume that it fills \[p\% \] of the tank.
Then, \[36 = \dfrac{p}{{100}} \times 40\]
\[ \Rightarrow \dfrac{{100 \times 36}}{{40}} = 90\% \]
Thus 36L of oil fills 90% of the 40L tank.
In (ii), Sam uses 3L of oil daily.
After 10 days we will have used \[3 \times 10 = 30L\] of oil
To calculate what percent of oil has been used
Assume that \[q\% \] of the oil has been used.
Then, \[30 = \dfrac{q}{{100}} \times 36\]
\[ \Rightarrow \dfrac{{30 \times 100}}{{36}} = 83.33\% \]

Thus, \[83.33\% \] of the oil in the 40L tank has been used.

Note:
While calculating percentages like these always use a variable like we have used in here (p, q). Read the question very clearly and write down the equations for the given information. In part (ii) of the question they have asked what percent of the oil in the 40L tank has been used. Do not confuse that.
You have to calculate what per-cent of 40 is 30, since the amount of oil in the 40L tank is only 36L not 40L.