Best Online CAT Coaching

Total Student = 140
Only cricket n(c)  = even numbered roll no
Last term = 140
a = first term = 2,  d = 2
140 = 2 + (n – 1)2
138/2 = n – 1
n = 70
n(c) = 70
No. of people who play Basketball but not cricket = {3,9,15,…..135}
Past term = 135,       a = 3, d = 6 
135 = 3 + ( n – 1) 6
132/6 = n – 1
n = 23
No. of people who play football but not cricket  = {5,15,25,35,…..135}
Last term = 135,   a = 5, d = 10
135 = 5 + (n – 1)10
130/10 = n – 1
n = 14
No. of people who play both Basketball & football have been added twice so we need to subtract them once 
No. of people playing both football & not cricket
= {15, 45,75,….135}
a = 15, d = 30    
Last term = 135
135 = 15 + (n – 1)30
120/30 = n – 1
n = 5
Student playing no sport = Total Number of Students – (Student playing only cricket + student playing Basketball not cricket +student playing football but not cricket – student playing Both Basketball & football but not cricket
= 140 – (70 + 23 + 14 – 5)
= 140 – 102
= 38