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Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is

Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is Correct Answer 20

Calculation:

Let M be the number of students choose mathematics as one of the subject

Let P be the number of students choose physics as one of the subject

Let C be the number of students choose chemistry as one of the subject

MPC + MP + MC = 23

⇒ MP + MC = 23 – 18

⇒ MP + MC = 5      ----(i)

Now, MPC + PM + PC = 25

⇒ PM + PC = 25 – 18

⇒ MP + PC = 7      ----(ii)

For smallest number of students who choose chemistry as one of subject in equation (i) and (ii) MP must be maximum and PC, MC must be non negative

Maximum value of MP in equation (i) and (ii) is 5 so that both equations satisfy and PC, MC must be non negative

Putting MP = 5 in equation (i)

MC = 0 

Putting MP = 5 in equation (ii)

PC = 2 

The smallest number of students who choose chemistry as one of subject = MPC + MC + PC

⇒ 18 + 0 + 2 

⇒ 20

∴  The smallest possible number of students who could choose chemistry as one of their subjects is 20

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