Question 1

The ratio of efficiency of A is to C is 5:3. The ratio of number of days taken by B is to C is 2:3. A takes 6 days less than C, when A and C completes the work individually. B and C started the work and left after 2 days. The number of days taken by…

Accepted Answer

A : C Efficiency 5 : 3 No of days 3x : 5x Given that, 5x-6 =3x => x = 3 Number of days taken by A = 9 Number of days taken by C = 15 B : C Days 2 : 3 Therefore, Number of days taken by B = 10 Work done by B and C in initial 2 days = 2 1 10 + 1 15 = 1/3 Thus, Rest work =2/3 Number of days required by A to finish 2/3 work = (2/3) x 9 = 6 days

Question 2

A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of …

Accepted Answer

Let the number of workers be x. Now, Using work equivalence method, X + (X-1) + (X-2)+ . . . . + 1 = X *55% of X => [X * (X+1)] / 2 = X * (55X/100) [because, Series is in AP. Sum of AP = {No. of terms (first term+ last term)/2} ] Therefore, X = 10

Question 3

(x-2) men can do a piece of work in x days and (x+7) men can do 75% of the same work in (x-10)days. Then in how many days can (x+10) men finish the work?

Accepted Answer

3 4 × ( x - 2 ) x = ( x + 7 ) ( x - 10 ) ⇒ x 2 - 6 x - 280 = 0 => x= 20 and x=-14 so, the acceptable values is x=20 Therefore, Total work =(x-2)x = 18 x 20 =360 unit Now 360 = 30 x k => k=12 days

Question 4

An air conditioner can cool the hall in 40 miutes while another takes 45 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room approximately ?

Accepted Answer

Let the two conditioners be A and B 'A' cools at 40min 'B' at 45min Together = (a x b)/(a + b) = (45 x 40)/(45 + 40) = 45 x 40/85 = 21.1764 = 22 min (approx).

Question 5

3 men, 4 women and 6 children can complete a work in 7 days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days ?

Accepted Answer

Let 1 woman's 1 day work = x. Then, 1 man's 1 day work = x/2 and 1 child's 1 day work x/4. So, (3x/2 + 4x + + 6x/4) = 1/7 28x/4 = 1/7 => x = 1/49 1 woman alone can complete the work in 49 days. So, to complete the work in 7 days, number of women required = 49/7 = 7.

Question 6

A is twice efficient as B and together they do the same work in as much time as C and D together. If C and D can complete the work in 20 and 30 daysrespectively, working alone ,then in how many days A can complete the work individually:

Accepted Answer

A + B = C + D | | | | Ratio of efficiency 10x + 5x 9x + 6x |________| |_________| 15x 15x Therefore , ratio of efficiency of A:C =10:9 Therefore, ratio of days taken by A:C = 9:10 Therefore, number of days taken by A = 18 days

Question 7

A is thrice efficient as B and C is twice as efficient as B. what is the ratio of number of days taken by A,B and C, when they work individually?

Accepted Answer

A : B : C Ratio of efficiency 3 : 1 : 2 Ratio of No.of days 1/3 : 1/1 : 1/2 or 2 : 6 : 3 Hence A is correct.

Question 8

A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6 AM and they work alternately for one hour each. When will the work be completed?

Accepted Answer

Work donee by A and B in the first two hours, working alternatively = First hour A + Second hour B = (1/4) + (1/12) = 1/3. Thus, the total time required to complete the work = 2 (3) = 6 days

Question 9

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days ?

Accepted Answer

Ratio of times taken by A and B = 100 : 130 = 10 : 13. Suppose B takes x days to do the work. Then, 10 : 13 :: 23 : x => x = ( 23 x 13/10 ) => x = 299 /10. A's 1 day's work = 1/23 ; B's 1 day's work = 10/299 . (A + B)'s 1 day's work = ( 1/23 + 10/299 ) = 23/299 = 113 . Therefore, A and B together can complete the work in 13 days.

Question 10

Two pipes A and B can fill a tank in 24 hours and 1717 hours respectively. Harihar opened the pipes A and B to fill an empty tank and some times later he closed the taps A and B , when the tank was supposed to be full. After that it was found that t…

Accepted Answer

Efficiency of Inlet pipe A = 4.16% 100 24 Efficiency of Inlet pipe B = 5.83% 100 17 1 7 Therefore, Efficiency of A and B together = 100 % Now, if the efficiency of outlet pipe be x% then in 10 hours the capacity of tank which will be filled = 10 * (10 - x) Now, since this amount of water is being emptied by 'C' at x% per hour, then 10 x 10 - x x = 2 . 5 h r s => x = 8 Therefore, in 10 hours 20% tank is filled only. Hence, the remaining 80% of the capacity will be filled by pipes A and B in 80/10 = 8 hours

Question 11

A does half as much work as Band C does half as much work as A and B together. If C alone can finish the work in 40 days, then together ,all will finish the work in ?

Accepted Answer

C alone can finish the work in 40 days. As given C does half as much work as A and B together => (A + B) can do it in 20 days (A + B)s 1 days wok = 1/20. A's 1 days work : B's 1 days Work = 1/2 : 1 = 1:2(given) A's 1 day’s work = (1/20) x (1/3) = (1/60) [Divide 1/20 in the raio 1:2] B's 1 days work = (1/20) x (2/3) = 1/30 (A+B+C)'s 1 day's work = (1/60) + (1/30) + (1/40) = 9/120 = 3/40 All the three together will finish it in 40/3 = 13 and 1/3 days.

Question 12

There are three boats B1, B2 and B3 working together they carry 60 people in each trip. One day an early morning B1 carried 50 people in few trips alone. When it stopped carrying the passengers B2 and B3 started carrying the people together. It took…

Accepted Answer

Combined efficiency of all the three boats = 60 passenger/trip Now, consider option(a) 15 trips and 150 passengers means efficiency of B1 = 10 passenger/trip which means in carrying 50 passengers B1 must has taken 5 trips. So the rest trips equal to 5 (10-5 = 5) in which B2 and B3 together carried remaining 250 (300 - 50 = 250) Passengers. Therefore the efficiency of B2 and B3 = 250/5 = 50 passenger/trip Since, the combined efficiency of B1, B2 and B3 is 60. Which is same as given in the first statement hence option(a) is correct.

Question 13

A, B and C can complete a piece of work in 24,6 and 12 days respectively.Working together, they will complete the same work in:

Accepted Answer

(A+B+C)'s 1 day's work = (1/24 + 1/6 + 1/12) = 7/24 so, A,B and C together will complete the work in 24/7 days.

Question 14

16 women can do a piece of work in 10 days while 15 men can do the same work in 12 days. All men and all women work alternately starting with all men, then find the time taken by them to complete the whole work?

Accepted Answer

Let efficiency of every man and every woman be 'm' unit/day and 'w' unit/day respectively 15×12×m = 10×16×w ⇒ m/w = 8/9 Total work = 15 × 12 × 9 = 1620 units In 2 days, total work done = 15 x 9 + 16 x 8 = 263 units So, in 10 days work done will be = 263 × 5 = 1315 units Remaining work will be done in = (1620-1315)/(15×8) = 5/2 days Total days = 10 5/2 days.

Question 15

When A, B and C are deployed for a task , A and B together do 70% of the work and B and C together do 50% of the work. who is most efficient?

Accepted Answer

A + B= 70% B + C =50% ∵ ( A + B ) + ( B + C ) - ( A + B + C ) = B => B= 20% A= 50% and C=30% Hence A is most efficient

Question 16

4 men can repair a road in 7 hours. How many men are required to repair the road in 2 hours ?

Accepted Answer

M x T / W = Constant where, M= Men (no. of men) T= Time taken W= Work load So, here we apply M1 x T1/ W1 = M2 x T2 / W2 Given that, M1 = 4 men, T1 = 7 hours ; T2 = 2 hours, we have to find M2 =? Note that here, W1 = W2 = 1 road, ie. equal work load. Clearly, substituting in the above equation we get, M2 = 14 men.

Question 17

A and B together can do a piece of work in 40 days. A having worked for 20 days, B finishes the remaining work alone in 60 days. In How many days shall B finish the whole work alone?

Accepted Answer

Let A's 1 day's work=x and B's 1 day's work=y Then x+y = 1/40 and 20x+60y=1 Solving these two equations , we get : x= 1/80 and y= 1/80 Therefore B's 1 day work = 1/80 Hence,B alone shall finish the whole work in 80 days

Question 18

If 2 men and 3 women can do a piece of work in 8 days and 3 men and 2 women in 7 days. In how many days can the work be done by 5 men and 4 women working together?

Accepted Answer

From the given data, => (2 M + 3W) 8 = (3M + 2W)7 => 16M + 24W = 21M + 14 W => 10W = 5M => 2W = M => 14W × ? = 7W × 8 ? = 4 days

Question 19

10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?

Accepted Answer

Given that (10M + 15W) x 6 days = 1M x 100 days => 60M + 90W = 100M => 40M = 90W => 4M = 9W. From the given data, 1M can do the work in 100 days => 4M can do the same work in 100/4= 25 days. => 9W can do the same work in 25 days. => 1W can do the same work in 25 x 9 = 225 days. Hence, 1 woman can do the same work in 225 days.

Question 20

A can finish a work in 18 days and B can do the same work in half the time taken by A. then, working together, what part of the same work they can finish in a day ?

Accepted Answer

A can do the work = 18 days B can do the work = 18/2 = 9 days (A + B)'s 1 day work = 1/18 + 1/9 = 1/6 => In 3 days = 3x1/6 = 1/2 work is completed.

Time and Work Questions