1. X takes 6 days less than Y to finish the work individually. If X and Y working together complete the work in 4 days, then how many days are required by Y to complete the work alone ?
A. 7 days
B. 10days
C. 5 days
D. 12days
E.None of these
Sol. Lets assume Y takes = a days
Then X will take = (a-6) days
Now given, 1/a + 1/(a-6) = 1/4
Solving, we get,
a = 12 days.
2. X and Y can complete a work in 20 days and 30 days respectively. They start the work and X left after some days. Now Z who can alone complete the same work in 20 days joined with Y and they completed the remaining work in 5 days. For how many days did Y work ?
A. 17
B. 18
C. 12
D. 15
E. None of these
Sol. Y worked for 5 days + the days after which X left.
Let X left after x days. so
(1/20)*x + (1/30)*(5+x) + (1/20)*5 = 1
Solve, x = 7
So Y worked for 5+7 days = 12 days.
3. 10 men and 6 women together can complete a piece of work in 6 days. The work done by a man in one day is double the work done by a woman in one day. If 10 men and 6 women started working and after 2 days, 4 men left and 4 new women joined them, in how many more days will the work be completed ?
A. 156/11
B. 136/11
C. 146/11
D. 126/11
E. None of these.
Sol. 1M = 2W
10 men and 6 women = 26 women
After 2 days : 6 Women + 4 Women +6 men = 22 Women
(26 * 6) / 1 = (26 * 2)/x
x = 1/3
(26 * 6) / 1/3 = (22 * x)/ 2/3
x = 156/11.
4. 5 men started the work and worked for 4 days. Now they are replaced by 12 women where 1 man can do as much work as 2 women do in 1 day. If the works gets completed in a total of 10 days, in how many days 7 women can complete the entire work ?
A. 20
B. 12
C. 16
D. 22
E. 14
Sol. Given 1 m = 2w, so 12 women = 6 men
Let 1 man do work in x days, so 1 man’s 1 day work = 1/x, so 5 men 1 day’s work = (1/x)*5
And since they did work for 4 days, so there work becomes (5/x)* 4 = 20/x
Now total work completed in 10 days, this mean that 12 women or 6 men did in (10-4) = 6 days
So similarly as above, 1 man’s 1 day work = 1/x, so 6 men 1 day’s work = (1/x)*6
And since they did work for 6 days, so there work becomes (6/x)* 6 = 36/x
So (20/x) + (36/x) = 1
Solve, x = 56
1 man do work in 56 days, so 1 woman in 2*56 days, and 7 women in (2*56)/7
5. A can do a piece of work in 10 days and B can do the same work in 15 days. They work together for 3 days then B left. Find in how many days A finish the remaining work ?
A. 4
B. 3
C. 5
D. 6
E. None of these
Sol. In 1 day working together they finish, 1/10 + 1/15 = 1/6th work.
In 3 days they will finish, = 1*3/6 = 1/2th work
Work remaining, to be done by A alone is = 1/2th work
A finihes the whole work in = 10 days
Thus, A will finish 1/2th work in = 10/2 = 5 days.
6. P and Q Working separately can do a piece of work in 6 days and 11 days, if they work alternately beginning with P then the work will be completed in how many days ?
A)10 days
B)6 days
C)8 days
D)5 days
E)None of these
Sol. Total work = 6*11 = 66
2 days(P+Q) = 1/6 + 1/11 = (11+6)/66 = 17/66
6 days(P+Q) = 51/66
Remaining work = (1-(51/66)) = 15/66
In 15, 6 done by P remaining done by Q (2 days)
6+2 = 8 days
7. A can complete a piece of work in 8 days and B can complete the work in 10 days and C in 12 days. B and C together worked for 3 days, then C left the work and A replaced him. In how many days will the remaining work be completed ?
A)1
B)2
C)3
D)4
E)None of these
Sol. (x-3)/8 + (x/10) + (3/12) = 1
(5x-15+4x)/40 = 1-3/12 = 12-3/12 = 9/12 = ¾
9x – 15 = 3*40/4 = 30
X = 45/9 = 5 (3days completed )
5 -3 = 2 days.
8. A can finish a piece of work in 24 days. B is 20% more efficient than A and C is 25% more efficient than B. Find the time B and C will take to finish the work?
A)7days
B)6days
C)8days
D)9days
E)None of these
Sol. A= 1/24
B = 120/100(1/24) = 1/20
C= 125/100(1/20) = 1/16
B+C =(1/20) + (1/16) = 16+20/320 = 36/320 = 8.88 = 9 days.
9. A total of 960 rupees is given to three people A, B and C. A and B together can complete 7/12 and C and B together can complete 5/12. So, how much amount should be given to A.
A) 360
B) 460
C) 280
D) 660
E) None of these
Sol. (work done by) : (work done by B and C)
A:B = 7:12 & C:B = 5:12 => A:B:C = 7:12:5
So amount to be paid to A = (7/24)*960 = 280.
10. 3 men and 4 women can complete a piece of work in 12 while the same is finished by 2 men and one woman in 15 days. A boy who is 25% less efficient than that of man can complete the piece of work in how many days.
A) 400/11
B) 420/11
C) 430/11
D) 450/11
E) None of these
Sol. 3m + 4w = 1/12
2m + w = 1/15. After solving we one day work of man = 33/900
One day work of the boy is= 75/100*(33/900) = 11/400. So no of days needed will be 400/11.
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