Question

6. un computer company requires 30 programmers to handle system programming jobs and 40 programmers to handle applications programming if the company appoints 55 programmers to carry out these jobs, how many of these perform jobs of both types? How many handle only system programming jobs? How many handle only applications programming?​

Answer 1

Answer: 15 programmers perform jobs of both types, 15 handle only system programming jobs and 25 handle only applications programming

Explanation: Let a, b and c be the number of people who handle both, only system programming, and only application programming jobs

We know that

a + b + c = 55 and

a + b = 30 ; a + c = 40

Adding the last 2 equations we get:

(a + b) + (a + c) = 30 + 40

⇒ a + (a + b + c) = 70

⇒ a + 55 = 70 ⇒ a = 70 - 55 = 15

b = 30 - a = 30 - 15 = 15

c = 40 - a = 40 - 15 = 25

Therefore a, b and c respectively are 15, 15 and 25