MAT Exam 2022 Paper

Concept:Use LCM of filling times to represent the total capacity of the tank.Explanation:Let tank capacity be $\mathrm{LCM}(12,15,20)=60$ units.In 1 hour, A fills $\frac{60}{12}=5$ units, B fills $\frac{60}{15}=4$ units, and C fills $\frac{60}{20}=3$ units.A is open all the time.First hour, A and B together fill $5+4=9$ units.Second hour, A and C together fill $5+3=8$ units.So in 2 hours, total work done $=9+8=17$ units.In 6 hours, work done $=17 \times 3=51$ units.Remaining work $=60-51=9$ units.In the 7th hour, A and B together fill exactly $9$ units.Hence the tank is filled in $6+1=7$ hours.Answer:Option A: 7 hours.