SSC CGL 201911)A can do 40% of a work in 12 days, whereas B can do 60% of the same work in 15 days. Both work together for 10 days. C completes the remaining work alone in 4 days. A, B and C together will complete 28% of the same work in :
2 days
A can do 40% of a work in 12 days, whereas B can do 60% of the same work in 15 days. Both work together for 10 days. C completes the remaining work alone in 4 days. A, B and C together will complete 28% of the same work in :
Let work be 1, A can do work in A days, B can do work in B days and C can do work in C days then
\({12\over A} = 0.4\), \({15 \over B} = 0.6\), A= 30 days, B = 25 days ; let C complete remaining work in 4 days after A and B works for 10 days
\( {10 \over 30}+{10\over 25}+ {4\over C} = 1\); C = 15 days.
Let the 28% work be completed in x days
\( {x \over 30}+{x\over 25}+ {x\over 15} = 0.28\)
Solve for x ; it will be 2 days
SSC CGL 202012)A, B and C can individually complete a task in 24 days,16 days and 32 days respectively. If A and C start the work and worked for 6 days and left, then the number of days required by B to complete the remaining task, is :
9
Let the total work be 96 units.
( LCM of 24, 16 and 32 is 96.)
Efficiency of A = work/time = 96/24 = 4;
Efficiency of B = 96/16 = 6;
Efficiency of C = 96/32 = 3;
Efficiency of A and C = 4 + 3 = 7;
Work done by A and C in 6 days = 7 x 6 = 42 units;
Remaining work = 96 - 42 = 54 units;
Time taken by B to complete 54 units work = 54/6 = 9 days
SSC CGL 202013)Eight persons can finish a work in 20 days. After 5 days they were requested to complete the work in the next 8 days. How many more persons should join the group to fulfil the requirement?
7
Total work = number of persons x time = 8 x 20 = 160;
Work done in 5 days = \( 8\times 5\) = 40;
Remaining Work = 160 - 40 = 120;
According to question,
Number of man x time = 120;
Number of man x 8 = 120;
Number of man = 120/8 = 15;
Number of persons should join the group = 15 - 8 = 7
SSC CGL 202014)A can do a piece of work in 6 days. B can do it in 9 days. With the assistance of C they completed the work in 3 days. In how many days can C alone do the work ?
18
C's 1 day's work = (A+B+C)'s 1 day's work - (A+B)'s 1 day's work = \({1\over3}-({1\over6}+{1\over9})={1\over18}\);
C, alone can do work in 18 days.
SSC CGL 202015)If 18 men can cut a field in 35 days, then in how many days can 21 men cut the same field?
30
\(M_1D_1=M_2D_2\); ⇒ 18 x 35 = 21 x \(D_2\); ⇒ \(D_2 =30 days\)
SSC CGL 202016)A contract is to be completed in 75 days and 187 men are to work 15 hours per day. After 65 days, \(3\over5\) of the work is completed. How many additional men should be employed, so that the work is completed in time, each man now working 17 hours per day?
528
Remaining work = \(1 - {3\over5} = {2\over5}\); Remaining time = 75 - 65 = 10 days; \({M_1D_1T_1\over W_1}={M_2D_2T_2\over W_2}\); ⇒ \({187\times65\times15\over{3\over5}}={M_2\times10\times17\over{2\over5}}\); ⇒ \(M_2=715\);
So number of additional men = 715 - 187 = 528
SSC CGL 202017)Ten men or twelve women can finish the same work in 10 days. If 5 men and 2 women undertake the work together, how many days will they take to complete the work?
15
Let the work be 1 and work done by 1 men in 1 day = \(1\over M\) & by 1 women in 1 day = \(1\over W\); then \({10\times10\over M} = 1\) ⇒ M = 100; & \({10\times12\over W}=1\) ⇒ W = 120;
Now let 5 men and 2 women complete the work in x days = \(x({5\over M}+ {2\over W})=1\); then put the value of M=100 & W = 120: then x = 15 days
SSC CGL 202018)A, B and C can individually complete a task in 20 days, 16 days and 30 days, respectively. If A and B started working on the task, and they worked for 4 days and left, then the number of days required by C to finish the remaining task is:
\(16 \frac{1}{2}\) days
Let the total work be 240 units. (LCM of 20, 16 and 30 is 240.)
Efficiency of A = total work/time taken to complete work = 240/20 = 12;
Efficiency of B = 240/16 = 15;
Efficiency of C = 240/30 = 8; Work done by A and B in 4 days = \(4 \times (12 + 15) = 4 \times 27\) = 108 units
Remaining work = 240 -108 = 132 units
Time taken by C to complete remaining work = 132/8 = \(16 \frac{4}{8} = 16 \frac{1}{2}\)
SSC CGL 202019)Amit and Sunil together can complete a work in 9 days, Sunil and Dinesh together can complete the same work in 12 days, and Amit and Dinesh together can complete the same work in 18 days. In how many days will they complete the work if Amit, Sunil and Dinesh work together?
8 days
One day's work of (Amit + Sunil + Dinesh) =\({1\over2}({1\over9}+{1\over12}+{1\over18})={1\over8}\); The work can be completed by all three together in 8 days.
SSC CGL 202020)A, B and C can individually complete a task in 24 days, 20 days and 18 days, respectively. B and C start the task, and they work for 6 days and leave. The number of days required by A alone to finish the remaining task is:
\(8{4\over5}\) days
Part of work done by B and C in 6 days = \(6({1\over20}+{1\over18})={19\over30}\); Remaining work = \(1-{19\over30}={11\over30}\); Time taken by A to complete the remaining work = \({11\over30}\times24=8{4\over5}\) days