"> Word Problem 4 | Job Exam Rare Mathematics (JEMrare)

Word Problem 4

Problem 4: In an exam 75% candidates pass in English, 65% candidates pass in Maths and 15% candidates fail both in English and Maths. If 495 candidates pass the exam, what number of candidates took the exam ?



Solution:

Let Total students =x

Pass in Eng = 75%

Fail in Eng = 25%

Pass in Maths=65%

Fail in Maths = 35%

Fail in both Eng & Maths=15%

Fail only in English=25-15=10%

Fail only in maths =35-15=20%

Now Total fail = Fail in English + Fail in Maths + Fail in both=10+20+15=45%

So, Total pass = 100-45=55%

55% of x =pass

55% of x =495

\frac{55}{100} of x=495

\frac{55}{100} \times x=495

Leaving ‘x’  on one side of equal sign’

 x=495\times \frac{100}{55}

 \Rightarrow x= 900