(a) Let students who take Engineering and Medical be 4b& b respectively Total students who take Commerce = (2a + 16) – (4b + b) = (2a + 16 - 5b) From A – 4b – (2a + 16 – 5b) = 8 – 2a + 9b = 24 … (i) Also,
b
(2a+16)
=
1
8
–2a + 8b = 16 … (ii) b = 8 Total students in Coaching Institute = 64 From B – (2a+16–5b)×
75
100
=4b … (i) 6a + 48 – 15b = 16b 31b = 6a + 48 b =
6a+48
31
So, statement A alone is sufficient to answer the question but statement B alone is not sufficient to answer the question.