Question

120 students have maths or science next lesson. There are 12 more boys than girls altogether. The ratio maths:science =2:3 half as many girls have maths as have science. A student is chosen at random. What is the probability that it is a boy who has maths?

Answer 1

66 girls 54 boys. 48 people do maths. 22 girls do maths. 48-22 = 26
26/120 = probability of boy with maths
26/120 = 13/60

Answer 2

To find : Probability of randomly choosing a boy having maths

Given : Total students = 120

• Let the number of girls be = G ; Let the number of boys be = B

Total , G = B + 120

G + B = 120

B + 12 + B = 120 ; 2B + 12 = 120

2B = 120 - 12 = 108

B = 108 / 2 = 54

G = 120 - 54 = 66

• Let Girls having maths = gm ; Let girls having science = gs

gm + gs = G , gm = 1/2 gs

1/2 gs + gs = G

3/2 gs = 66

gs = 66 x 2 / 3

gs = 22 x 2 = 44

gm = 22

• Maths : Science Students = M : S = 2x , 3x

2x + 3x = 120

5x = 120

x = 120 / 5 = 24

M = 24 x 2 = 48 ; S = 24 x 3 = 72

• Probability ( Boy having Maths ) :

Boys having maths = Total students having maths M - Girls having maths gm = 48 - 22 = 26

Hence, Probability (Boy having Maths) =  26 / 120 = 13 / 60

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