Question

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 1

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