Question

Out of $80$ students $45\%$, students passed in Mathematics and $60\%$ students passed in English. If $35\%$ students failed in both the subjects, how many students passed in both the subjects?

Answer 1

Find number of students passed in both the subjects:

Total number of students$=80$

Students passed in Mathematics

$$\begin{gathered} =45\% \\ =\frac{45}{100}\times 80 \\ =36 \end{gathered}$$

Students passed in English

$$\begin{gathered} =60\% \\ =\frac{60}{100}\times 80 \\ =48 \end{gathered}$$

Students failed in both subjects$=35\%$

Thus, the number of students passed

$$\begin{gathered} =80–35\%\mathrm{of}80 \\ =80–\frac{35}{100}\times 80 \\ =80–28 \\ =52 \end{gathered}$$

Now, the number of students passed in both subjects

$$\begin{gathered} =36+48–52 \\ =32 \end{gathered}$$

Hence, $32$ students passed in both the subjects.