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

Answer: (a)

A tap can fill the tank in 6 hours. In filling the tank to its half, time required = 3 hours.

Remaining part = $1/2$

Since, 1 tap takes 6 hours to fill the tank

Time taken by 4 taps take to fill $1/2$ of the tank

= $6/4 × 1/2 = 3/4$ hour

Total time = $3 + 3/4$

= $3{3}/4$ hours = 3 hours 45 minutes

Answer: (b)

A, B and C together fill the tank in 6 hours.

Part of the tank filled in 1 hour by (A + B + C) = $1/6$

Part of the tank filled in 2 hours by all three pipes

= $2/6 = 1/3$

Remaining empty part

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

This $2/3$ part is filled by (A + B).

Time taken by (A + B) to fill the fully empty tank

= ${7 × 3}/2 = 21/2$ hours

Part of tank filled by C in 1 hour

= $1/6 - 2/21 = {7 - 4}/42 = 3/42 = 1/14$

∴ Required time = 14 hours.

Answer: (a)

Let the capacity of the tank = x litres

According to the question,

Quantity of water emptied by the leak in 1 hour = $x/10$ litres

Qunatity of water filled by the tap in 1 hour = 240 litres

According to the question,

$x/10 - x/15$ = 240

${3x - 2x}/30 = 240$

$x/30$ = 240

$x$ = 240 × 30 = 7200 litres

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: (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: (a)

Using Rule 7,

Part of tank filled by both the pipes in 1 hour

= $1/4 - 1/16 = {4 - 1}/16 = 3/16$

Required time = $16/3 = 5{1}/3$ hours