out of 7500 candidates , 75% offerer English and 45% offered Maths . How many offered both ?

Question

(A)1000 (B)1750 (C)2000 (D)1500 (E)2500

Answer 1

75% of 7500=5625 and 45% of 7500=3375.

Let E=number of English only candidates and M=number of maths only candidates. Let X be the number offered both, then E+X+M=7500; we know that E+X=5625 and M+X=3375. Therefore E+X+M+X=(E+M+X)+X=5625+3375=9000. We know E+M+X=7500, so 7500+X=9000, and X=1500.

Therefore 1500 candidates were offered both. [Also 4125 were offered English only and 1875 were offered maths only.]

Answer 2

(75+45)%-100%=20%

20% of 7500=1500