2000 candidates appear in a written test in mathematics and general aw

1.	2000 candidates appear in a written test in mathematics and general awareness for a government job.1800 passed in at least one subject. If 1200 passed in mathematics and 1500 in general awareness .find how many passed in mathematics only ?
Answer» Step-by-step explanation: $\bf{\underline{\underline\red{Given:-}}}$ 2000 candidates appeared in a WRITTEN TEST in mathematics and GENERAL awareness. 1800 passed in at least one subject. 1200 passed in mathematics 1500 passed in general awareness. $\bf{\underline{\underline\blue{To\:Find:-}}}$ The number of candidates passed in only mathematics. $\bf{\underline{\underline\green{Solution:-}}}$ Let M be the number of candidates passed in Mathematics. And GA be the number of candidates passed in General Awareness. 1800 students passed in at least 1 subject. So:- M U GA = 1800 [U = UNION] Candidates passed in only Mathematics = 1200 → M = 1200 Candidates passed only in General awareness = 1500 → GA = 1500 → M + GA = 1200 + 1500 = 2700 Number of students passed in both = (M + GA) - (M U GA) = 2700 - 1800 = 900 ∴ Number of candidates passed in both = 900 ∴ M ⋂ GA = 900 Number of candidates passed only in Mathematics. = M - (M ⋂ GA) = 1200 - 900 = 300 ∴ 300 candidates are passed only in Mathematics

2000 candidates appear in a written test in mathematics and general awareness for a government job.1800 passed in at least one subject. If 1200 passed in mathematics and 1500 in general awareness .find how many passed in mathematics only ?

Answer»

Step-by-step explanation:

2000 candidates appeared in a WRITTEN TEST in mathematics and GENERAL awareness.

Let M be the number of candidates passed in Mathematics.

And GA be the number of candidates passed in General Awareness.

1800 students passed in at least 1 subject.

So:-

M U GA = 1800 [U = UNION]

Candidates passed in only Mathematics = 1200

→ M = 1200

Candidates passed only in General awareness = 1500

→ GA = 1500

→ M + GA = 1200 + 1500 = 2700

Number of students passed in both

= (M + GA) - (M U GA)

= 2700 - 1800

= 900

∴ Number of candidates passed in both = 900

∴ M ⋂ GA = 900

Number of candidates passed only in Mathematics.

= M - (M ⋂ GA)

= 1200 - 900