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RD Sharma Solutions Class 8 Mathematics Solutions for Time and Work Exercise 11.1 in Chapter 11 - Time and Work

Question 27 Time and Work Exercise 11.1

A cistern has two inlets A and B which can fill it in 12 hours and 15 hoursrespectively. An outlet can empty the full cistern in 10 hours. If all the three pipesare opened together in the empty cistern, how much time will they take to fill thecistern completely?

Answer:

The given details are,

Inlet A can fill the cistern in = 12 hours

Inlet A can fill the cistern in 1 hour = 1/12

Inlet B can fill the cistern in = 15 hours

Inlet B can fill the cistern in 1 hour = 1/15

Outlet pipe can empty the cistern in = 10 hours

Outlet pipe can empty the cistern in 1 hour = 1/10

So we have, (1/12 + 1/15) – 1/10

= (9/60) – 1/10

= (9-6)/60

= 3/60

= 1/20 part

∴ When all 3 pipes are opened together to empty the cistern, time taken to fill the cistern completly = 1/(1/20) = 20 hours

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