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

Answer: (a)

Using Rule 1 and 2,

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

= $1/30 + 1/45 = {3 + 2}/90 = 1/18$ part

Part of tank filled in 12 minutes

= $12/18 = 2/3$ part

Remaining part

= $1 - 2/3 = 1/3$ part

When pipe C is opened,

Part of tank filled by all three pipes

= $1/30 + 1/45 - 1/36$

= ${6 + 4 - 5}/180 = 5/180 = 1/36$

Time taken in filling $1/3$ part

= $1/3$ × 36 = 12 minutes

Total time = 12 + 12 = 24 miuntes

Answer: (b)

Part of the tank filled in first 2 hours

= $1/4 + 1/6 = {3 + 2}/12 = 5/12$ Part

Part of the tank filled in first 4 hours

= ${2 × 5}/12$ parts= $5/6$ parts

Remaining part = $1 - 5/6 = 1/6$

Now it is the turn of pipe A

Time taken to fill $1/4$ part = 1 hour

Time taken to fill $1/6$ part

= $1/6 × 4 = 2/3$ hour

Total time = 4 + $2/3 = 4{2}/3$ hours

Answer: (d)

Part of the tank filled by

(A + B + C) in 1 hour = $1/6$

Part of tank filled by these in 2 hours

= $2/6 = 1/3$

Remaining part = $1 - 1/3 = 2/3$

Time taken by A and B in filling

$2/3$ rd part = 8 hours

Time taken by A and B in filling the whole tank

= ${8 × 3}/2$ = 12 hours

Part of tank filled by C in an hour

= $1/6 - 1/12 = 1/12$

Hence, required time = 12 hours

Answer: (a)

Pipe A fills the tank in $75/2$ minutes.

Part of the tank filled by A in 30 minutes

= $2/75 × 30 = 4/5$

Remaining part

= $1- 4/5 = 1/5$

Now, 1 part is filled by pipe B in 45 minutes

$1/5$ part is filled in

= 45 × $1/5$ = 9 minutes

Hence, the pipe B should be turned off after 9 minutes.

Answer: (a)

Using Rule 7,

Let the inflow fill the tank in x hours.

$1/x - 1/{2x} = 1/36$

[leakage being half of inflow]

= ${2 - 1}/{2x} = 1/36$

2x = 36

$x = 36/2$ = 18 hours

Answer: (b)

Part filled by A and B in 1 hour

= $1/12 + 1/15 = {5 + 4}/60 = 3/20 +$...(i)

Part filled by A and C in the next 1 hour

= $1/12 + 1/20 = {5 + 3}/60 = 2/15$

Part filled in 2 hours

= $3/20 + 2/15 = {9 + 8}/60 = 17/20$

Part filled in 6 hours = $51/60$

Remaining part

= $1 - 51/60 = 9/60 = 3/20$

This part will be filled by (A+B) in 1 hour. [By (i)]

Total time taken = 7 hours