In a company, 35% of employees are from a science background and \(\frac{1}{5}\)th are from an arts background. The rest are either illiterate or with a commerce background. The number of illiterate is 300 which is \(\frac{1}{2}\) of the commerce background.

How many employees are from science or arts background?

Given:

35% of employees are from a science background.

\(\dfrac{1}{5}\) of employees are from an arts background.

The number of illiterate employees is 300, which is \(\dfrac{1}{2}\) of the commerce background.

Formula used:

Total employees = Science + Arts + Illiterate + Commerce

Illiterate = \(\dfrac{1}{2} \times Commerce\)

Calculation:

Let the total number of employees be x .

Science employees = 0.35x

Arts employees = \(\dfrac{1}{5}x\) = 0.2x

Illiterate employees = 300

Commerce employees = 2 × Illiterate employees = 2 × 300 = 600

Total employees = Science + Arts + Illiterate + Commerce

⇒ x = 0.35x + 0.2x + 300 + 600

⇒ x = 0.55x + 900

⇒ x - 0.55x = 900

⇒ 0.45x = 900

⇒ x = \(\dfrac{900}{0.45}\)

⇒ x = 2000

Employees from science or arts background = Science + Arts

⇒ 0.35 × 2000 + 0.2 × 2000

⇒ 700 + 400

⇒ 1100

∴ The correct answer is option 1.