1.A and B can do a work in 12 days, B and C in 15 days and C and A in 20 days. If A, B and C work together, they will complete the work in :
A.5 days B. 6 days C. 10 days D. 15 days [SSC-99,03,06,11,13]
Correct Answer: C
According to question, A and B can do a work in 12 days
=> (A + B)’s one day’s work = 1/ 12
Similarly, (B + C)’s one day’s work = 1/ 15 and (C + A)’s one day’s work = 1 /20
=> On adding all three,
2 (A + B + C)’s one days’s work = 1/12+1/15+1/20 = (10+8+6)/120= 1/ 5
=> (A + B + C)’s one days’s work = 1/ 10
=>A, B and C together can finish the whole work in 10 days.
2.A particular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to complete the job if the two teams work together?
A.4 days B. 6 days C. 9 days D. 18 days [SSC -27.02.2000]
Correct Answer: A
According to question, 10 men’s one day’s work = 1/ 12
=>1 man one day’s work =1/( 12*10) =1/ 120
Similarly, 1 woman one day’s work =1/(6* 10)= 1/ 60
=>(1 man + 1 woman)’s one day’s work = 1/120+1/60 = (1+2)/120=3/ 120= /1 40 => (10 men + 10 women)’s one day’s work =10/ 40= 1/ 4
Therefore, both the teams can finish the whole work in 4 days.
3.While working 7 hours a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, working 8 hours a day ?
A.3 days B. 4 days C. 2.5 days D. 3.6 days [SSC -27.07.2008]
Correct Answer: A
A alone can complete the work in 42 days working 1 hour daily.
Similarly, B will take 56 days working 1 hour daily.
A ’s 1 day’s work = 1/ 42 ,B ’s 1 day’s work = 1/ 56
=>(A + B) ’s 1 day’s work = 1/ 42+ 1/ 56 = (4+ 3)/ 168= 7/ 168
Time taken by (A + B) working 8 hours daily = 168/( 7* 8) = 3 days
4.A and B working together; can do a piece of work in 9/ 2 hours. B and C working together can do it in 3 hours. C and A working together can do it in 9/ 4 hours. All of them begin the work at the same time. Find how much time they will take to finish the piece of work.
A.3 hours B. 2 hours C. 2·5 hours D. 3·25 hours [SSC-11]
Correct Answer: B
(A + B)’s 1 hour’s work = 2/ 9 …..(i),
(B + C)’s 1 hour’s work = 1 /3 ……(ii)
(C + A)’s 1 hour’s work = 4/ 9 …..(iii)
Adding all three equations, 2 (A + B + C)’s 1 hour’s work = 2/ 9+ 1/ 3+ 4/ 9=( 2+3+4)/ 9 = 1 => A, B and C together will complete the work in 2 hours.
5.A can do as much work as B and C together can do. A and B can together do a piece of work in 9 hours 36 minutes and C can do it in 48 hours. The time (in hours) that B needs to do the work alone, is :
A.18 hrs B. 24 hrs C. 30 hrs D. 12 hrs [SSC -13]
Correct Answer: B
9 hours 36 minutes = 9+ 36/ 60= 48/5 hours
(A + B)’s 1 hour’s work = 5/ 48 ,C’s 1 hour’s work = 1/ 48
(A + B + C)’s 1 hour’s work = 5/ 48 +1 /48= 1/ 8 …..(i)
A’s 1 hours work = (B + C)’s 1 hour’s work …..(ii)
From equations (i) and (ii), 2 × (A’s 1 hour’s work) = 1/ 8, A’s 1 hour’s work = 1 /16 , B’s 1 hour’s work = 5 /48-1/ 16 =( 5- 3)/ 48 = 1/ 24 => B alone will finish the work in 24 hours.
6. A can do a piece of work in 12 days and B in 15 days. They work together for 5 days and then B left. The days taken by A to finish the remaining work is
A.3 B. 5 C. 10 D. 12 [SSC -14]
Correct Answer: A
Work done by A and B in 5 days = 5( 1/ 12+ 1/ 15)= 5{(5+ 4)/ 60 }= 5*( 9/ 60)= 9/ 12= 3/ 4 So,Remaining work = 1- 3/ 4= 1/ 4 ,Therefore, Time taken by A = 12/4=3 days
7.A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all the three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is
A.100 B. 96 C. 95 D. 90 [SSC-14]
Correct Answer: B
Time taken by B and C = x days (let)
So,Time taken by A = 3x days and Part of work done by A, B and C in 1 day = 1/ x + 1/ 3x = (3+ 1)/ 3 x = 4 3x
Therefore, 4/ 3x = 1 /24 = 3x = 4 × 24 => x = 32 days
Hence, Time taken by A = 32 × 3 = 96 days
8.A can do 1 4 of a work in 10 days. B can do 1 3 of the work in 20 days. In how many days can both A and B together do the work ?
A.30 days B. 32 days C. 24 days D. 25 days [SSC-14]
Correct Answer: C
Since A does 1/ 4 work in 10 days hence A will do 1 work in 10 × 4 = 40 days
Similarly, B will do the same work in 20 × 3 = 60 days
So, (A + B)’s 1 day’s work = 1 /40 + 1/ 60 = (3+ 2)/ 120 = 5/ 120 = 1 /24
Therefore, Required time = 24 days
9.15 men take 20 days to complete a job working 8 hours a day. The number of hours a day should 20 men take to complete the job in 12 days
A.5 hours B. 10 hours C.15 hours D. 18 hours [SSC-14]
Correct Answer: B
We know that, M1× D1× T1 = M2× D2× T2 => 15 × 20 × 8 = 20 × 12 × T2 =>T2 =(15 × 20 × 8)/ (20 × 12 ) = 10 hours
10.How many men need to be employed to complete a job in 5 days, if 15 men can complete 1 3 of the job in 7 days ?
A.20 B. 21 C.45 D. 63 [SSC-14]
Correct Answer: D
15 men complete 1 3 work in 7 days. => Time taken in doing 1 work = 3 × 7 = 21 days
We know that,M1D1 = M2D2=> 15 × 21 = M2 × 5 => M2 = 63 days
11.A’s 2 days’ work is equal to B’s 3 days’ work. If A can complete the work in 8 days then to complete the work B will take
A.14 days B.12 days C. 15 days D.16 days [SSC-15]
Correct Answer: B
A’s 2 days’ work = B’s 3 days’ work =>Time taken by A = 8 days , Time taken by B = (8/ 2) × 3 = 12 days
12.If 90 men can do a certain job in 16 days, working 12 hours per day, then the part of that work which can be completed by 70 men in 24 days, working 8 hours per day is
11.1 /3 B. 2/ 3 C. 7/ 9 D. 5/ 8 [SSC-15]
Correct Answer: C
Using, M1× D1× T1× W2 = M2× D2× T2×W1=>7/ 9 parts
13.A and B together can do a piece of work in 9 days. If A does thrice the work of B in a given time, the time A alone will take to finish the work is
A.4 days B.6 days C. 8 days D. 12 days [SSC-16]
Correct Answer: D
Let time taken by A be x days. So,Time taken by B = 3x days
According to the question, 1/x+1/3x = 1/ 9 => 3x = 4 × 9 => x = 12 days
14.A can do as much work in 4 days as B can do in 5 days, and B can do as much work in 6 days as C in 7 days. In what time will C do a piece of work which A can do in a week ?
A.10( 5/ 24) days B. 4 (4/ 5) days C. 6( 8/ 15) days D.12( 6/ 19) days [SSC-16]
Correct Answer: A
A’s 4 days’ work = B’s 5 days’ work => A : B = 4 : 5 Again, B : C = 6 : 7
So,A : B : C = 4 × 6 : 5 × 6 : 5 × 7 = 24 : 30 : 35
Since, Time taken by A = 7 days hence,Time taken by C = 35 24 × 7 = 245/ 24=10( 5/ 24) days
15.A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the job ?
A.50 days B.60 days C. 48 days D. 54 days [SSC-03,13]
Correct Answer: B
(A+B)’s 1 day’s work = 1/30 =>(A + B)’s 20 day’s work = (20/30- 2/3)
Remaining work =1- 2/ 3=1/ 3
Now, 1/ 3 part of work is done by A in 20 days. So, Whole work will be done by A alone in 20 × 3 = 60 days.
16.8 men can do a work in 12 days. After 6 days of work, 4 more men were engaged to finish the work. In how many days would the remaining work be completed?
A.2 B. 3 C. 4 D. 5 [SSC-03]
Correct Answer: C
Work done by 8 men in 6 days = 6/ 12= 1/ 2
Remaining work = 1-1/2= 1/ 2
4 more men are engaged. So, total number of men = 8 + 4 = 12
By work and time formula
M1× D1× W2 = M2× D2×W1= >8× 12× 1/2 = 12× D2×1=>D2=4 days
17.A certain number of persons can complete a piece of work in 55 days. If there were 6 persons more, the work could be finished in 11 days less. How many persons were originally there ?
A.17 B. 24 C.30 D. 22 [SSC-03]
Correct Answer: B
Originally, let there be x men
Now, more men, less days
(x + 6) : x : : 55 : 44 So, (x+6)/x=55/44 or 5x = 4x + 24 or x = 24
18.A and B working separately can do a piece of work in 10 days and 15 days respectively. If they work on alternate days beginning with A, in how many days will the work be completed ?
A.18 days B. 13 days C. 12 days D. 6 days [SSC-03]
Correct Answer: C
Work done by 2 (A + B) in one day = 1/ 10 + 1/15 = 5/ 30= 1/ 6
So,Work done by (A + B) in one day = 1 /12
(A + B) can complete the work in 12 days
19.A and B can do a piece of work in 20 days and 12 days respectively. A started the work alone and then after 4 days B joined him till the completion of the work. How long did the work last ?
A.10 days B. 20 days C. 15 days D. 6 days [SSC-04]
Correct Answer: A
A’s 1 day’s work = 1 /20 =>A’s 4 days’ work = = 4/ 20= 1/ 5
Remaining work = 1 – (1 /5 )=4/ 5
This part is completed by A and B together. Now, (A + B)’s 1 day’s work = 1/ 20+ 1/ 12 = 8/ 60=2 /15 Now, 2/ 15 work is done by (A + B) in 1 day.
So, 4/ 5 work is done in = ´ 15/ 2* 4/ 5 = 6 days.
Hence, the work lasted for 4 + 6 = 10 days.
20.16 women take 12 days to complete a work which can be completed by 12 men in 8 days. 16 men started working and after 3 days 10 men left and 4 women joined them. How many days will it take them to complete the remaining work ?
A.4 B. 6 C.8 D. 10 [SSC-2014]
Correct Answer: B
Work done by 12 men in 8 days= Work done by 16 women in 12 days.
=>12 × 8 men = 16 × 12 women => 1 man =>2 women
Now, work done by 12 men in 1 day = 1/8
1 man’s 1 day’s work = 1/( 12* 8) = 1/ 96
So,16 men’s 3 day’s work
= (16* 3)/96 =1/2
Remaining work = 1- 1/2 = 1/ 2
Now, 1/ 2 work is done by 6 men and 4 women.
So, 6 men + 4 women = (6 + 2) men = 8 men
Using, M1× D1× W2 = M2× D2×W1= >8× 12× 1/2 = 12× D2×1=6 days.
21.If 12 men or 24 boys can do a work in 66 days, the number of days in which 15 men and 6 boys can do it is
A.44 B. 33 C.55 D. 66 [SSC-14]
Correct Answer: A
Since 12 men =24 boys
Hence 1 man =2 boys
15 men + 6 boys = 30 boys + 6 boys = 36 boys
M1D1 = M2D2 =>24 × 66 = 36 × D2=> D2 = 44 days
22.A certain number of men can do a piece of work in 40 days. If there were 45 men more the work could have been finished in 25 days. Find the original number of men employed in the work.
A.70 B. 85 C. 65 D. 75 [SSC-14]
Correct Answer: D
Original number of men = x (let)
M1D1 = M2D2 => x × 40 = (x + 45) × 25 => 8x = (x + 45) × 5 =>8x = 5x + 225 => 8x – 5x = 225 => 3x = 225 => x = 225/ 3 = 75 men
23.12 men can complete a work in 90 days. 30 days after they started work, 2 men left and 8 men joined. How many days will it take to complete the remaining work ?
A.90 days B. 60 days C. 40 days D. 50 days [SSC-16]
Correct Answer: C
Work done in 30 days = W2
, M1× D1× W2 = M2× D2×W1=>12× 90× W2 = 12× 30×1=>W2=1/3
Remaining work = 1 –1/3 = 2/ 3
New number of , M1× D1× W2 = M2× D2×W1=>12× 90× 2/3 = 18× D2×1=>D2=40 days.
24.If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?
A.4 days B.5 days C. 3 days D. 2 days [SSC-14]
Correct Answer: C
3m = 6w So,1m = 2w
12m + 8w = (12 × 2w) + 8w = 32w
So, 6 women can do the work in 16 days.
Hence, 32 women can do the work in (16 ×6) /32= 3 days
25.If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?
A.260 B. 240 C. 280 D. 520 [SSC-99]
Correct Answer: A
10 men = 20 boys
So, 1 man = 2 boys
Therefore, 8 men + 4 boys = (16 + 4) boys = 20 boys Hence, 8 men and 4 boys will make 260 mats in 20 days.
Z26.3 men and 4 boys can complete a piece of work in 12 days. 4 men and 3 boys can do the same work in 10 days. Then 2 men and 3 boys can finish the work in
A.35/ 2 days B.60/ 11 days C. 8 days D. 22 days [SSC-12]
Correct Answer: A
12 (3 men + 4 boys) = 10 (4 men + 3 boys) => 36 men + 48 boys = 40 men + 30 boys => 4 men = 18 boys => 2 men = 9 boys
So, 4 men + 3 boys= 21 boys, who do the work in 10 days and 2 men + 3 boys = 12 boys
M1D1 = M2D2 => 21 × 10 = 12 ×D2 => D2 = 35/2 days
26.If 4 men or 6 women can do a piece of work in 12 days working 7 hours a day; how many days will it take to complete a work twice as large with 10 men and 3 women working together 8 hours a day? (1) 6 days
A.7 days B. 8 days C. 10 days D.12 days [SSC-13]
Correct Answer: A
4 men =6 women
1 men = 6/ 4= 3/ 2 = women
10 men + 3 women = 10*3/ 2 +3= 18 women
M1× D1×T1× W2 = M2× D2×T2×W1=>6×12×7×2 = 18× D2×8×1
=>D2=7 days.
27.A man is twice as fast as a woman and a woman is twice as fast as a boy in doing a work. If all of them, a man, a woman and a boy can finish the work in 7 days, in how many days a boy will do it alone ?
A.49 B.7 C. 6 D. 42 [SSC-14]
Correct Answer: A
According to the question, 1 man = 2 women = 4 boys
1 man + 1 woman + 1 boy = (4 + 2 +1) boys = 7 boys
M1 D1 = M2 D2 => 7 × 7 = 1 × D2 => D2 = 49 days
28.12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is
A.2 : 1 B. 3 : 1 C.1 : 3 D.5 : 4 [SSC-16]
Correct Answer: A
Work done by 12 men + 16 boys in 5 days = Work done 13 men + 24 boys in 4 days
=> (60 men + 80 boys)’s 1 day’s work = (52 men + 96 boys)’s 1 day’s work
=>(60 – 52) men = (96 – 80) boys
=> 8 men = 16 boys
=> 1 man =2 boys
Hence, Required ratio = 2 : 1
29.3 men and 5 women can do a work in 14 days while 5 men can do it in 14 days. 5 men and 5 women can complete the work in
A.13 days B. 11 days C.10 days D. 12 days [SSC-17]
Correct Answer: C
Since, 5 men can do 1 work in 14 days.
Hence,3 men will do 3 5 work in 14 days.
Remaining work = 1- 3/ 5= 2/ 5
So, 5 women do 2 5 work in 14 days.
Therefore, Time taken by 5 women in doing 1 work = 14* 5/ 2= 35 days
So, (5 men + 5 women)’s 1 day’s work = 1/ 14+ 1/ 35 =(5+ 2) /70 =7 /70= 1/ 10
Hence, Required time = 10 days.
30.P can complete 1/4 of a work in 10 days, Q can complete 40% of the same work in 15 days, R, completes 1/3 of the work in 13 days and S, 1/6 of the work in 7 days. Who will be able to complete the work first ?
A.P B. Q C. R D. S [SSC-10]
Correct Answer: B
Time taken by P in completing 1 work = 10 × 4 = 40 days
Time taken by Q in completing 1 work = 15* 5/ 2= 75/ 2 days
Time taken by R in completing 1 work = 13 × 3 = 39 days
Time taken by S in completing 1 work = 7 × 6 = 42 days
Clearly, Q took the least time i.e. 75 /2 days
31.Two workers A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work than when work together. If B worked alone, would take 9/2 hours more than when work together. The time required to finish the work together is
A.5 hours B.4 hours C. 8 hours D. 6 hours [SSC-15]
Correct Answer: D
Time taken by A and B = x hours (let).
According to the question, Time taken by A alone = (x + 8) hours.
Time taken by B alone = x + 9 /2 hours.
So, [{1/( x + 8)} + 1/{x+( 9/ 2)}] = 1/x
By solving we will get, x = = 6 hours
32.A, B and C are employed to do a piece of work for Rs. 5,290. A and B together are supposed to do 19/23 of the work and B and C together 8/23 of the work. Then A should be paid
A.Rs. 4,250 B. Rs. 3,450 C. Rs. 1,950 D. Rs. 2,290 [SSC-14,15]
Correct Answer: B
Part of work done by A and B = 19/23
So, Part of work done by C = 1 – 19/23 = 4/ 23
Part of work done by B and C = 8 /23
Part of work done by B = 8/ 23 – 4 /23 = 4 /23
So, Part of work done by A = 19/ 23 – 4/ 23 = 15/ 23
Hence, Ratio of the shares of wages of A, B and C = 15/23 : 4/ 23 : 4 /23 = 15 : 4 : 4
Therefore, A’s share = 15/ 23 × 5290 = Rs. 3450
33.A can do a certain job in 12 days. B is 60% more efficient than A. Then B can do the same piece of work in
A.8 days B. 15/2 days C. 25/ 4 days D. 6 days [SSC-16]
Correct Answer: B
A can do a work in 12 days. B is 60% more efficient than A.
So,Time taken by B = 100/ 160*12 days = 15/ 2 days
34.A, B and C contract a work for Rs. 440. A and B together are to do 9/ 11 of the work. The share of C should be :
A.Rs. 75 B. Rs. 90 C. Rs. 100 D. Rs. 80 [SSC-16]
Correct Answer: D
Work done by A and B together = 9/ 11 parts
So, Work done by C = 1 -9 /11 =2/ 11 parts
Total amount = Rs. 440
So, C’s share = Rs. (2 /11 ) 440 = Rs. 80
35.A can do a piece of work in 70 days and B is 40% more efficient than A. The number of days taken by B to do the same work is
A.40 days B. 60 days C. 50 days D. 45 days [SSC-12]
Correct Answer: C
A : B = D2 : D1 => 100 : 140 = D2 : 70 => 100 × 70 = 140 ×D2 => D2 = 100 *70 /140 =50 days.
36.To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it ?
A.30 days B. 35 days C. 40 days D. 45 days [SSC-07]
Correct Answer: A
Let B alone can do the work in x days.
So, A can do the work in 3x/ 2 days.
According to the question,
(1/x)+(2/3x)=1/18=>x= 30 days
37.A and B together can do a work in 12 days. B and C together do it in 15 days. If A’s efficiency is twice that of C, then the days required for B alone to finish the work is
A.60 days B. 30 days C. 20 days D.15 days [SSC-11]
Correct Answer: C
(A + B)’s 1 day’s work = 1/12 ………. (i)
(B + C)’s 1 day’s work = 1/15 ………. (ii)
Difference between A and C’s 1 day’s work = 1 /12 – 1/ 15 = (5 -4 )/60 =1 /60
If A alone completes the work in x days, C will do the same in 2x days.
So, 1/x-1/2x=1/60=>x = 30
Hence,B’s 1 day’s work
= 1/ 12 -1 /30 – [From equation (i)]
= (5 -2 )/60= 3/ 60 =1 /20
Hence, B alone will complete the work in 20 days
38.A is thrice as good a workman as B and is, therefore, able to finish a piece of work in 60 days less than B. The time (in days) in which they can do it working together is
A.22 days B. 45/2 days C.23 days D.93/ 4 days [SSC-99,05,11,12]
Correct Answer: B
If A completes the work in x days, B will do the same in 3x days.
So,3x – x = 60 =>2x = 60 => x = 30 and 3x = 90
So, (A + B)’s 1 day’s work = 1 /30 -1 /90= (3+ 1)/ 90 = 4/ 90= 2/ 45
Hence, A and B together will do the work in 45/ 2 days
39.A does 20% less work than B. If A can complete a piece of work in 15/2 hours, then B can do it in
A.13/2 hours B.6 hours C. 7hours D.5 hours [SSC-06,13]
Correct Answer: B
A does 20% less work than B.
Ratio of time taken = 5 : 4
A completes a work in 15 /2 hours
Time taken by B to do the same work
= 15 /2* 4/ 5 = 6 hours.
40.Kamal can do a work in 15 days. Bimal is 50 per cent more efficient than Kamal in doing the work. In how many days will Bimal do that work?
A.14 days B. 12 days C. 10 days D. 21/2 days [SSC-02,06]
Correct Answer: C
Efficiency and time taken are inversely proportional Bimal : Kamal = 150 : 100 (work) =>100 : 150 (Time) = 2 : 3
Since, 3 units => 15 days
So,2 units Þ 15/ 3* 2 = 10 days
Hence, Bimal complete the work in 10 days
41. A is thrice as good a workman as B and therefore is able to finish a job in 40 days less than B. Working together, they can do it in
A.14 days B. 13 days C. 20 days D.15 days [SSC-11]
Correct Answer: D
Time taken by A to complete the work = x days
So, Time taken by B to complete the work = 3x days
So, 3x – x = 2x = 40 => x = 20 and 3x = 60
Therefore, (A + B)’s 1 day’s work = 1/ 20 +1 /60 =(3 +1)/ 60 = 4/ 60 =1 /15
A and B together will complete the work in 15 days.
41.A is 30% more efficient than B, and can alone do a work in 23 days. The number of days, in which A and B, working together can finish the job is
A.11 days B. 13 days C. 20 days D.21 days [SSC-11]
Correct Answer: B
Time taken by B = 130 /100 *23 =299 /10 days
(A + B)’s 1 day’s work = 1/ 23+ 10 /299 =( 13 +10)/ 299 = 23/ 299 =1 /13
Time taken by (A + B) = 13 days
43.Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require
A.26/ 5 days B.25/4 days C.15/2 days D.35/4 days [SSC-13]
Correct Answer: B
If A alone does the work in x days and B alone does the work in y days,
then 1/x+1/y =1/5 …..(i)
Again, 2/x+1/3y =1/3 ….(ii)
By equation (ii) × 3 – (i),
6/x+1/y-1/x-1/y=1-1/5
=>x=25/4 days.
44.Two persons can complete a piece of work in 9 days. How many more persons are needed to complete double the work in 12 days?
A.3 B. 2 C. 4 D. 1 [SSC-06]
Correct Answer: A
Here, M1 = 2, W1 = 1, D1 = 9 M2 = ?, W2 = 2, D2 = 12
M1D1W2 = M2D2W1 =>2 × 9 × 2 = M2 × 12 × 1 M2 => M2 = 3
45.3 men and 7 women can do a job in 5 days, while 4 men and 6 women can do it in 4 days. The number of days required for a group of 10 women working together, at the same rate as before, to finish the same job is :
A.30 days B. 36 days C. 40 days D. 20 days [SSC-13]
Correct Answer: D
3 × 5 men + 7 × 5 women
= 4 × 4 men + 6 × 4 women
=> 16 men – 15 men = 35 women – 24 women
So, 1 man = 11 women
=> 3 men + 7 women = 40 women
M1D1 = M2D2 => 40 × 5 = 10 × D2 => D2 = 20 days
46.Suman can do a work in 3 days. Sumati can do the same work in 2 days. Both of them finish the work together and get 150. What is the share of Suman ?
A.30 B. 60 C. 70 D. 75 [SSC-99]
Correct Answer: B
Ratio of Suman’s and Sumati’s 1 day’s work = 1/ 3: 1/ 2 = 2/ 3
Sum of the ratios = 2 + 3 = 5
Suman’s share = ´ 2/ 5* 150 =Rs. 60
47.A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for 3200. With the help of C they completed the work in 3 days. How much is to be paid to C ?
A.375 B. 400 C.600 D. 800 [SSC-04]
Correct Answer: B
A’s 1 day’s work = 1/ 6
B’s 1 day’s work = 1/ 8
(A + B + C)’s 1 day’s work = 1/ 3
So, C’s 1day’s work = 1/ 3– 1/ 6– 1/ 8 = 1 /24
Ratio of their one day’s work respectively = 1/ 6: 1/ 8: 1/ 24 = 4 : 3 : 1
Sum of the ratios = 4 + 3 + 1 = 8
Hence,C’s share = 1/ 8 × 3200 =Rs. 400
48.If 5 men or 7 women can earn 5,250 per day, how much would 7 men and 13 women earn per day ?
A.11,600 B. 11,700 C.16,100 D.17,100 [SSC-10]
Correct Answer: D
5 men = 7 women [Both earn same amount in 1 day]
So,7 men =7 /5 * 7 = 49/ 5 women
So,7 men + 13 women = 49 /5 + 13 = 114 /5 women
Now, Since 7 women = 5250
So,11/4 5 women = 5250/ 7* 114/ 5 = Rs.17,100
49.2 men and 1 woman can complete a piece of work in 14 days while 4 women and 2 men can do the same work in 8 days. If a man gets Rs. 180 per day, then a woman will get per day
A.Rs. 150 B. Rs. 140 C. Rs. 120 D. Rs. 160 [SSC-14]
Correct Answer: C
(2 men + 1 woman)’s 14 days’ work = (4 women + 2 men)’s 8 days’ work
=> 28 men + 14 women = 32 women + 16 men
=> (28 – 16) = 12 men =(32 – 14) = 18 women
=>2 men = 3 women
So, 1 woman = 2/ 3 man
Since, Wages per day of 1 man = Rs. 180
Wages per day of 1 woman = 2/ 3 × 180 = Rs. 120
50.The daily wages of A and B respectively are Rs.3.50 and Rs. 2.50. When A finishes a certain work, he gets a total wage of Rs. 63. When B does the same work, he gets a total wage of Rs.75. If both of them do it together what is the cost of the work ?
A.Rs. 67.50 B. Rs. 27.50 C. Rs. 60.50 D. Rs. 70.50 [SSC-16]
Correct Answer: A.
Time taken by A = 63/ 3.50 = 18 days
Time taken by B = 75 2.5 = 30 days
(A + B)’s 1 day’s work = 1/ 18 + 1/ 30 = 4/ 45
Required time = 45 /4 days
Therefore, Total wages = Rs. 45 4 × (3.50 + 2.50)=Rs.67.5
51.A farmer can plough a field working 6 hours per day in 18 days. The worker has to work how many hours per day to finish the same work in 12 days ?
A.7 hrs B. 9 hrs C.11 hrs D.13 hrs [SSC-13]
Correct Answer: B.
D1 T1 = D2 T2 Þ 18 × 6 = 12 × T2
T2=9 hrs
52.150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped on the second day, four more workers dropped on third day and so on. It takes 8 more days to finish the work now. Find the number of days in which the work was completed?
A.28 B. 24 C.25 D.30 [SSC-15]
Correct Answer:C.
Let 150 workers complete the work in x days.
So, 150 × x = 150 + 146 + …. to (x + 8) terms
On putting x = 17
LHS = 150 × 17 = 2550
RHS = 150 + 146 + …. to 25 terms
a = 150, d = –4, n = 25
We know that,
S = n 2 [2a + (n–1) d] = 25/ 2 [2 × 150 + 24 × (–4)] = 2550
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