Model 3 Opening both taps and leaks Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Work done in 1 hour by the filling pump = $1/2$

Work done in 1 hour by the leak and the filling pump = $3/7$

Work done by the leak in 1 hour

= $1/2 - 3/7 = {7 - 6}/14 = 1/14$

Hence, the leak can empty the tank in 14 hours.

Answer: (d)

Using Rule 1,

Part of the cistern filled in 2 hours by pipe A and B

= $2(1/6 + 1/8) =2({4 + 3}/24) = 7/12$

Remaining part =$1 - 7/12 = 5/12$

Time taken by pipe B in filling $5/12$ part

= $5/12 × 8 = 10/3 = 3{1}/3$ hours

Answer: (c)

Using Rule 7,

Part of tank filled by inlet pipe in 1 hour

= $1/6 - 1/8 = {4 - 3}/24 = 1/24$

Hence, if there is no leak, the inlet pipe will fill the tank in 24 hours.

Capacity of the tank

= 24 × 60 × 4 = 5760 litres

Answer: (c)

Part of the cistern filled by pipes A, B and C in 1 hour = $1/6$

Part of the cistern filled by all three pipes in 2 hours = $1/3$

Remaining part =$1– 1/3 = 2/3$

Now, pipe A and B fill $2/3$ part of the cistern in 7 hours

Pipe A and B will fill the cistern in ${7 × 3}/2 = 21/2$ hours

Part of the cistern filled by Aand B in 1 hour = $2/21$

So Part of the cistern filled by C in 1 hour = $1/6 - 2/21$

= ${7 - 4}/42 = 1/14$

Pipe C will fill the cistern in 14 hours.