Blog

Parin Sir > Quantitative Aptitude (Maths) > Time and Work > Examples 9 to 13 of time and work > Examples 9 to 13 of time and work

Examples 9 to 13 of time and work

August 17, 2020
Category: Examples 9 to 13 of time and work

No Comments

(9) If two pipes function simultaneously, the reservoir will be filled in 18 hours. One pipe fills the reservoir 15 hours faster than the other. How many hours does it take the second pipe to fill the reservoir ?

Soln. Let the reservoir be filled by first pipe in x hours.

Then, second pipe will fill it in ( x + 15 ) hours.

∴ $\frac{1}{x} + \frac{1}{\left(\mathrm{x\ }+\mathrm{\ 15}\right)} = \frac{1}{18}$

∴ $\frac{\mathrm{x\ }+\mathrm{\ 15\ }+\mathrm{\ x}}{\mathrm{x\ }(\mathrm{\ x\ }+\mathrm{\ 15\ })} = \frac{1}{18}$

∴ x² – 21 x – 270 = 0

∴ ( x – 30 ) ( x + 9 ) = 0

∴ x = 30.

( neglecting the – ve value of x )

So, the second pipe will take ( 30 + 15 ) hrs i.e., 45 hrs. to fill the reservoir.

(10) A and B working separately can do a piece of work in 15 and 25 days respectively. If they work for a day alternately, (i) A beginning and (ii) B beginning, in how many days, the work will be completed ?

Soln. ( A + B )’s 2 day’s work = $\frac{8}{75}$

∴ Work done in 9 pairs of days = $\frac{72}{75} = \frac{24}{25}$

Remaining Work = 1 – $\frac{24}{25} = \frac{1}{25}$

A’ s 1 day’s work = $\frac{1}{15}$

B’ s 1 day’s work = $\frac{1}{25}$

∴ ( A + B )’s 2 day’s work = $\frac{8}{75}$

(i) A beginning : –

If $\frac{1}{15}$ of work completed by A in 1 day

∴ $\frac{1}{25}$ “ “ “ (?) “

$\frac{1}{25} \times 1 \times \frac{15}{1}$ = $\frac{3}{5}$ days.

If A is beginning the work will complete in $\left[(9\times2)+\frac{3}{5}\right] = 18\frac{3}{5}$ days.

(i) B beginning : –

If $\frac{1}{25}$ of work completed by B in 1 day

$\therefore \ \frac{1}{25}$ “ “ “ (?) “

$\frac{1}{25} \times 1 \times \frac{25}{1}$ = 1 day

If B is beginning the work will complete in $\left[(9\times2)+1\right]$ = 19 days.

(11) A can do a piece of work in 10 days and B can finish it in 15 days. They work together for 2 days and then A goes away. In how many days will B finish the work ?

Soln. ( A + B )’s 2 days’ work + B’s x day’s work = 1

∴ $2\left(\frac{1}{10}+\frac{1}{15}\right) + x \left(\frac{1}{15}\right)$ = 1

∴ $\frac{2(3+2)+x(2)}{30}$ = 1

∴ x = 10 days

(12) Two pipes A and B can fill a cistern in 10 minutes and 15 minutes respectively. If both the pipes are opened together, then after how many minutes should A be closed so that the tank is full in 9 minutes ?

Soln. Let A be closed after ‘x’ minutes.

Then, x $\left(\frac{1}{10}+\frac{1}{15}\right) + ( 9 - x )\frac{1}{15}$ = 1.

⇒ x = 4 minutes.

(13) Two pipes can fill a cistern in 21 hours and 24 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom it took 48 minutes more to fill the cistern. When the cistern is full, in what time will the leak empty it ?

Soln. Work done by the two pipes in 1 hour = $\left(\frac{1}{21}+\frac{1}{24}\right)$ = $\frac{15}{168} = \frac{5}{56}.$