Model 1 Basic Pipes & Cisterns problems Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Part of the cistern filled in 1 hour = $1/8$

Part of the cistern emptied in 1 hour = $1/16$

When both the taps are opened simultaneously, part of cistern filled in 1 hour

= $1/8 - 1/16 = {2 - 1}/16 = 1/16$

Hence, the cistern will be filled in 16 hours.

Using Rule 7,

Here, x = 8, y = 16

Required time = ${xy}/{y- x}$

= ${8 × 16}/{16 - 8}$ = 16 hours

Answer: (c)

Part of the tank filled by pipes A and B in 1 minute

= $1/36 + 1/45 = {5 + 4}/180$

= $9/180 = 1/20$

Part of the tank filled by these pipes in 7 minutes

= $7/20$

Remaining unfilled part

= $1 - 7/20 = {20 - 7}/20 = 13/20$

When all three pipes are opened.

= $1/20 - 1/30 = {3 - 2}/60 = 1/60$

Time taken in filling $13/20$ part

= $13/20$ × 60 = 39 minutes

Required time = 39 + 7 = 46 minutes

Answer: (c)

If pipe y be closed after x minutes, then

$18/24 + x/32$ = 1

$x/32 = 1 - 18/24 = 1- 3/4 = 1/4$

$x = 32/4$ = 8 minutes

x = 24, y = 32, t = 18

Required time = $[y(1 –{t/x})]$ minutes

= $[32(1 - {18/24})]$ minutes

= $[32(1 - {3/4})] = 32 × 1/4$ = 8 minutes

Answer: (d)

Let x be number of pumps

9 : 6 : : 12 : x = 12 : 15 : : 12 : x

9 × 12 × x = 6 × 12 × 15

$x = {6 × 12 × 15}/{9 × 12}$ = 10

Answer: (a)

Using Rule 2 and 7,

Part of the cistern filled in 1 hour

when pipes P and S are open

= $1/4 - 1/10 = {5 - 2}/20 = 3/20$

Hence, the cistern will be filled in $20/3$ hours ≈ 6.6 hours

Part of the cistern filled in 1 hour

when pipes P, R and S are open

= $1/4 + 1/12 - 1/10$

= ${15 + 5 - 6}/60 = 14/60 = 7/30$

Hence, the cistern will be filled in $30/7$ hours ≈ 4.3 hours

Part of the cistern filled in I hour

when pipes P, Q and S are open

= $1/4 + 1/8 - 1/10$

= ${10 + 5 - 4}/40 = 11/40$

Hence, the cistern will be filled in $40/11$ hours ≈ 3.6 hours

Cistern can be filled faster when P, Q & S are open

Answer: (c)

Using Rule 7,

Part of the cistern filled by pipe Q in 1 minute

= $1/20 - 1/30 = {3 - 2}/60 = 1/60$

Required time = 60 minutes