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Examples 5 to 8 of time and work
(5) A cistern has two taps which fill it in 10 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 30 minutes. How long will the waste pipe take to empty the full cistern ?
Solution.
Let, the waste pipe empty the tank in x hrs, then
Net part filled in 1 hour = =
Thus, waste pipe empty the tank in 7.5 hrs.
(6) A is thrice as good a workman as B and is therefore able to finish a piece of work in 40 days less than B. Find the time in which they can do it, working together.
Solution.
Ratio of work done by A and B in same time = 3 : 1.
Ratio of times taken to finish the same work = 1 : 3.
A can finish the work in k days and while B can finish it in 3k days.
3 k – k = 40 k = 20
A can finish the work in 20 days and while B can finish it in 60 days
( A + B )’s 1 day’s work =
=
=
.
Hence, both together can finish the work in = 15 days.
(7) A can do a piece of work in 40 days. B is 60 % more efficient than A. Find the number of days it takes B to do the same piece of work.
Soln. The ratio of work of A and B = 100 : 160 = 5 : 8
∴ The ratio for days for them = 8 : 5
∴ For A, 8 k = 40
∴ k = 5
Now, For B, 5 k = 5 ( 5 ) = 25 days.
(8) A & B can do a piece of work in 24 days; B & C in 30 days; C & A in 40 days. In how many days will they finish it together and separately ?
Soln. (A + B)’s 1 day’s work = ; (B + C)’s =
; (C + A)’s work =
∴ [ ( A + B ) + ( B + C ) + ( C + A ) ] ‘s 1 day’s work =
∴ 2 ( A + B + C )’s 1 day’s work =
∴ ( A + B + C )’s 1 day’s work = \frac{1}{20}.
↦ So, they together can finish the work in 20 days.
A’s 1 day’s work = [( A + B + C )’s 1 day’s work ] – [( B + C )’s work ]
=
∴ A alone can finish the work in 60 days.
Similarly, B’s 1 day’s work =
∴ B alone can finish the work in 40 days.
And, C’s 1 day’s work =
∴C alone can finish the work in 120 days.
