Question

In a basket of apples 12% of them are rotten and 66 are in good condition. Find the total number of apples in the basket.
A) 75
B) 70
C) 71
D) 80

Answer 1

Hint:: To solve this type of problem first of all we have to calculate the total no. of rotten apples in the basket and then to calculate the final answer that means, total no. of apples. For getting that, we have to add the total no. of rotten apples and good apples i.e.,
Total no. of apples = No. of good apples + no. of rotten apples.

Complete step by step solution:
First, we have to calculate the total no. of rotten apples so as per the question,
It is given that $12\% $ are rotten apples and $66$apples are in good condition.
So, the total no. of rotten apples will be $12\% $ of total no. of apples.
Then, Percentage of good apples will be
 [Total percentage ( \[100{\text{ }}\% \]) $ - $ rotten apple percentage ($12\% $) ]
$ = 100 - 12\% = 88\% $
If \[88\% \]of total no. of apples is $66$.
Then , \[1{\text{ }}\% \] of total no. of apples would be – \[\dfrac{{66}}{{88}}\]
Then \[100{\text{ }}\% \]of total no. of apples will be – \[\dfrac{{66}}{{88}} \times 100 = \dfrac{3}{4} \times 100 = 25 \times 3 = 75\]
So, for calculating the total no. of apple we have to get \[100{\text{ }}\% \] of the total no. of apples that will include both no. of rotten apples and no. of good apples.

$\therefore$ The total no. of apples will be $75$. Hence, the correct option is (A).

Note:
First of all, read the question carefully to understand what they asked for. We can use two different methods to calculate the answer to this type of question This method is easier and understandable than any other method.
Alternative method:
To solve the problem, we need to find the no. of rotten apples using a given percentage of it in total no. of apples & then add it to the no. of good apples to get the total no. of apples in the basket.
$12\% $ of total no. of apples –
  \[Percentage{\text{ }}of{\text{ }}rotten{\text{ }}apples{\text{ }} \times {\text{ }}no.{\text{ }}of{\text{ }}good{\text{ }}apples{\text{ }}/{\text{ }}percentage{\text{ }}of{\text{ }}good{\text{ }}apples\]
\[12 \times \dfrac{{66}}{{88}} = 12 \times \dfrac{3}{4} = 3 \times 3 = 9\]
Now, Total no. of apples = no. of rotten apples + no. of good apples
$ = 9 + 66 = 75$
So, you can use either of these methods to get the answer according to your convenience but make sure you don’t make a mistake in calculations.