Two pipes can fill a cistern in 28 and 21 hours respectively and an another pipe can empty 30 gallons of water per hour. All the three pipes working together can fill the empty cistern in 84 hours. What is the capacity (in gallons) of the cistern?

Let total capacity of cistern (in gallons) = $$x$$

=> Efficiency of both inlet pipes respectively = $$(\frac{x}{28}+\frac{x}{21})$$ gallons/hr

Similarly, efficiency of outlet pipe = $$-30$$ gallons/hr

According to ques,

=> $$(\frac{x}{28}+\frac{x}{21}-30)\times84=x$$

=> $$\frac{3x+4x-(30\times84)}{84}=\frac{x}{84}$$

=> $$7x-(30\times84)=x$$

=> $$7x-x=6x=30\times84$$

=> $$x=\frac{30\times84}{6}$$

=> $$x=5\times84=420$$ gallons

=> Ans - (C)