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Parin Sir > Quantitative Aptitude (Maths) > Time and Work > Examples 1 to 4 of time and work > Examples 1 to 4 of time and work

Examples 1 to 4 of time and work

August 17, 2020
Category: Examples 1 to 4 of time and work

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(1) A can build a wall in 40 days, which B alone can build in 50 days. If they build it together and get a payment of Rs. 1125, what is B’s share ?

Solution.

Ratio of their Days = 40 : 50 = 4 : 5

Ratio of their shares = Ratio of their work = 5 : 4.

B’s share = Rs. $\left ( 1125\times\frac{4}{9} \right )$ = Rs. 500.

(2) A can finish a piece of work in 8 days while B can do it in 20 days. If both work at it together, what time will they take to do the work

Solution.

A’s 1 day’s work = $\frac{1}{8}$ ; B’s 1 day’s work = $\frac{1}{20}$ .

$\therefore$ ( A + B )’s 1 day’s work = $\frac{1}{8}$ + $\frac{1}{20}$ = $\frac{7}{40}$ .

Time taken by both to finish the work = $\frac{40}{7}$ days = $5\frac{5}{7}$ days.

(3) Two pipes A and B can fill a tank in 12 hours and 16 hours respectively. Find the time taken to fill the tank when both the pipes are turned on simultaneously.

Solution.

A’s 1 hour’s work = $\frac{1}{12}$ & B’s 1 day’s work = $\frac{1}{16}$ .

( A + B )’s 1 day’s work = $\frac{1}{12}$ + $\frac{1}{16}$ = $\frac{7}{48}$ .

Thus, both the pipes together can fill the tank in $\frac{48}{7}$ = $6\frac{6}{7}$ hours.

(4) Pipe A can fill a tank in 10 hours while pipe B alone can fill it in 20 hours and pipe C can empty the full tank in 30 hours. If all the pipes are opened together, how much time will be needed to make the tank full ?

Solution.

Net part filled in 1 hour = $\left (\frac{1}{10} + \frac{1}{20} - \frac{1}{30} \right )$ = $\frac{7}{60}$ .