One day work of A = $\displaystyle \frac{1}{12}$, B = $\displaystyle \frac{1}{18}$
Working together A and B can complete = $\displaystyle \frac{1}{12} + \frac{1}{18} = \frac{3 + 2}{36} = \frac{5}{36}$ = 7 $\displaystyle \frac{1}{5}$ days.
Or
$\displaystyle \frac{12 \times 18}{12 + 18} = \frac{12 \times 18}{30} = \frac{36}{5}$ = 7 $\displaystyle\frac{1}{5}$ days.
$\displaystyle \frac{xy}{x + y}$
As Somu is twice as efficient as Jai then efficiency ratio will be = 2 : 1 ratio or [units]
Working together Somu and Jai can complete 2 + 1 = 3 units in a day
Total work = 18 x 3 = 54 units.
Somu = $\displaystyle \frac{54 \ \text{units}}{2 \ \text{units}}$ = 27 days
Jai = $\displaystyle \frac{54 \ \text{units}}{1 \ \text{unit}}$ = 54 days
Let one day work of Rekha can complete 3 units of work, while Jaya can 1 unit
Rekha + Jaya = 3 + 1 = 4 units in a day, total = 24 x 4 = 96 units.
Rekha alone $\displaystyle \frac{96}{3}$ = 32 days, Jaya = $\displaystyle \frac{96}{1}$ = 96 days.
Therefore Jaya takes 96 â€“ 32 = 64 days more then Rekha.
B alone = $\displaystyle \frac{1}{2} \left((A + B)+(B + C)â€“(A + C)\right) = \frac{1}{2} \left(\frac{1}{15} + \frac{1}{18} - \frac{1}{24} \right)$
= $\displaystyle \frac{1}{2} \left(\frac{24 + 20 - 15}{360} \right) = \frac{1}{2} \left(\frac{29}{360} \right) = \frac{29}{720} = 24 \frac{24}{29}$ days.
If the work starts with Veeru.
Two days work of Jai and Veeru = $\displaystyle \frac{1}{15} + \frac{1}{20} = \frac{7}{60}$ th part.
In 16 days 8 $\displaystyle \frac{7}{60} = \frac{56}{60}$ th part.
On 17th day Veeruâ€™s turn $\displaystyle \frac{56}{60} + \frac{1}{20} = \frac{59}{60}$ th part.
Remaining work = 1 â€“ $\displaystyle \frac{59}{60} = \frac{1}{60}$ th part.
On 18th day Jaiâ€™s turn as Jai can complete the work in 15 days then $\displaystyle \frac{1}{60}$ th part in.
$\displaystyle \frac{1}{60} \times 15 = \frac{1}{4}$ th day, therefore the work will be completed in = 17 $\displaystyle \frac{1}{4}$ days.
One day work of Man = $\displaystyle \frac{1}{12}$, working together by Man and Woman = $\displaystyle \frac{1}{10}$
Woman alone = $\displaystyle \frac{1}{12} - \frac{1}{10} = \frac{5 - 6}{60} = \frac{1}{60}$ = 60 days.
Amount sharing ratio = Efficiency ratio.
Time Ratio = Man : woman = 12 : 60 or 1 : 5.
But efficiency ratio will be in inverse proportion to the time ratio.
Therefore efficiency ratio Man to Woman = 5 : 1
Man = 12,000 $\displaystyle \times \frac{5}{6}$ = Rs.10,000; Women = 12,000 $\displaystyle \times \frac{1}{6}$ = Rs.2,000.
Number of personâ€™s required to complete the work in 24 days, with as equally capable as 45 is
$\displaystyle M_2 = \frac{M_1 \times D_1}{D_2} => \frac{45 \times 72}{24}$ = 135 persons are required, but with 1 $\displaystyle \frac{1}{2}$ efficiency
135 Ã· 1 $\displaystyle \frac{1}{2}$ = 90 or 90 persons.
=> $\displaystyle M_2 = \frac{M_1 \times D_1}{D_2} = M_2 = \frac{12 \times 24}{18}$ = 16 or 16 persons.
The work completed by A and B in one day is = $\displaystyle \frac{1}{12} + \frac{1}{16} = \frac{4 + 3}{48} = \left(\frac{7}{48} \right)^{th}$ part.
In 3 days = $\displaystyle 3 \left(\frac{7}{48} \right) = \left(\frac{21}{48} \right)^{th}$ part.
Remaining = 1 - $\displaystyle \frac{21}{48} = \left(\frac{27}{48} \right)^{th}$ part.
B can complete in $\displaystyle \frac{27}{48} \times$ 16 = 9 days.
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Un-Attempted Questions | |
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Total Wrong Answers |
1. If A can complete a work in â€˜nâ€™ number of days then in one day the work completed by A is $\displaystyle \frac{1}{n}$ part of work.
2. If, in one day A can complete $\displaystyle \frac{1}{n}$ th part of work then total work would be completed in â€˜nâ€™ number of days.
Note: Here â€˜nâ€™ denotes time, it can be Days/Hours/Minutes.
3. If A can complete a work in â€˜xâ€™ days while B can complete the same work in â€˜yâ€™ days. Then working together A and B can finish the work in one day = $\displaystyle \left(\frac{x + y}{xy}\right)^ {th}$ part, then total work = $\displaystyle \left(\frac{xy}{x + y}\right)$ days.
4. If â€˜mâ€™ number of personâ€™s can complete a work in â€˜nâ€™ number of days. Then working alone 1 person can complete the work in m x n = mn days.
5. If A and B working together can complete a work in â€˜xâ€™ days, if A alone can complete the work in â€˜yâ€™ days, then B alone can complete the work in = $ \displaystyle \frac{1}{x} - \frac{1}{y} = \frac{xy}{x - y} $ days.
6. A and B can complete a work in â€˜xâ€™ days, B and C can complete the same work in â€˜yâ€™ days, A and C can complete the same work in â€˜zâ€™ days. Then working together A, B and C can complete the work in 1 day = $\displaystyle \frac{1}{2} \left(\frac{1}{x} + \frac{1}{y} + \frac{1}{z}\right)$ = $\displaystyle \frac{1}{2} \left(\frac{yz + xz + xy}{xyz}\right) $
Note: The same rules are also applicable to Pipes & Cisterns.
7. M_{1} x D_{1} = M_{2} x D_{2}
M = Number of Persons
D = Number of days / hours / Minutes
M_{2} = $\displaystyle \frac{M_1 \times D_1}{D_2}$
D_{2} = $\displaystyle \frac{M_1 \times D_1}{M_2}$
The workerâ€™s left after
$\displaystyle \frac{M_1 \times D_1 - M_2 \times D_2}{M_1 - M_2}$
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