UPSC NDA I 2016 Mathematics Solved Paper

Let A, B & C be the sets of numbers divisible by 10,15 & 25 respectively
No. divisible by 10=100=n(A)
No. divisible by 15=66=n(B)
No. divisible by 25=40=n(C)
No. divisible by (10&15)=33=n(A∩B)
No. divisible by (15&25)=13=n(B∩C)
No. divisible by (25&10)=20=n(A∩C)
No. divisible by (10,15&25)=6=n(A∩B∩C)
No. divisible by 10,15‌and‌25=n(A∪B∪C)
Thus, no. which are neither divisible by 10 nor 15 nor
25=1000−146=854