Question

How many students students failed in Physics and Maths?

• A. 65
• B. 18
• C. 58
• D. 47
• E. Inadequate data

Answer 1

The correct option is A 65

Number of students $=280$
Cleared Maths $=185$
Cleared Physics $=210$
Cleared Chemistry $=222$
Students who passed in Maths and Physics $=180$
Students who passed in Maths and Chemistry $=175$
Students who passed in Physics and Chemistry $=200$
Number of students who passed in atleast one subject $=280-47=233$

$x+w+180\dots \left(i\right)$
$w+z=200\dots \left(ii\right)$
$w+y=175\dots \left(iii\right)$
$M+x+w+y=185\dots \left(iv\right)$
$P+x+w+z=210\dots \left(v\right)$
$C+y+w+z=222\dots \left(vi\right)$
$M+P+C+y+x+z+w=233\dots \left(vii\right)$
By Eqs:- $\left(iv\right)+\left(v\right)\left(vi\right)-\left(vii\right)$
$x+y+z+2w=384$
By Eqs:- $\left(i\right)+\left(ii\right)+\left(iii\right)$
$x+y+z+3w=555\dots \left(ix\right)$
$\left(ix\right)-\left(viii\right)\times w=171$
From Eq. (i) $x=9$
From Eq. (ii) $z=200-717=29$
From Eq. (iii) $y=175-171=4M=185-4-9-171=1P=210-9-171-29=1C=222-4-29-171=18$

Required answer $=47+18=65$