Time and Work problems
- 1. A can finish a work in 15 days and B can do the same work in 12 days . B worked for 8 days and left the job .In how many days, A alone can finish the remaining work?
Options- A. 6 days
- B. 5 days
- C. 4 days
- D. 3 days Discuss
Correct Answer: 5 days
Explanation:
B's 8 days work=(1/12) x 8 = 2/3
Reaining work= 1/3
Now, 1/15 work is done by A in 1 day
Therefore, 1/3 work is done by A in 15 x (1/3) = 5 days
- 2. In a public bathroom there are n taps 1,2,3...n. Tap1 and Tap2 take equal time to fill the tank while Tap3 takes half the time taken by Tap2 and Tap4 takes half the time taken by Tap3. Similarly each next number of tap takes half the time taken by previous number of Tap i.e, K-th Tap takes half the time taken by (K-1)th Tap. If the 10th tap takes 2 hours to fill the tank alone then what is the ratio of efficiency of 8th tap and 12th tap, respectively?
Options- A. 4:1
- B. 5:3
- C. 16:1
- D. 1:16 Discuss
Correct Answer: 1:16
Explanation:
Time taken by 8th tap = 2 x 2 x 2= 8 hours
Time taken by 12th tap = 2x (1/2) x (1/2) = 1/2 hour
Ratio of time taken by 8th tap and 12th tap = 8 : 1/2 =16:1
Therefore, Ratio of efficiencies of 8th tap and 12th tap =1:16
- 3. Two persons Shyam and Rahim can do a job in 32 days together. Rahim can do the same job in 48 days alone. They started working together and after working 8 days Rahim is replaced by a third person Ram whose efficiency is half that of Rahim. Find in how many days the remaining work will be completed by both Shyam and Ram together?
Options- A. 16 days
- B. 72/5 days
- C. 15 days
- D. 96/5 days Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, IT Trainer
Correct Answer: 72/5 days
Explanation:
Work done by Shyam and Rahim in 8 days = 8/32 = 1/4
Remaining work to be done by Shyam and Ram = 1 - 1/4 = 3/4
Given efficieny of Ram is half of Rahim i.e, as Rahim can do the work in 48 days, Ram can do the work in 24 days.
One day work of Ram and Shyam = (1/32 - 1/48) + 1/24 = 5/96
Hence, the total work can be done by Shyam and Ram together in 96/5 days.
Therefore, remaining work 3/4 can be done by them in 3/4 x 96/5 = 72/5 = 14.4 days.
- 4. If a soldier fires 7 shots from a gun in 12 minutes then find the total number of shots fired by the man in 3/2 hrs.
Options- A. 45
- B. 44
- C. 46
- D. 47 Also asked in: GATE, CAT, Bank Exams, AIEEE, IT Trainer, Database Administrator, Bank PO, Bank Clerk, Analyst
Correct Answer: 46
Explanation:
Here given soldier shots 7 shots in 12 min
=> 1 shot doen't take any time in 12 min
=> Only 6 shots take 12 min
12 min ------ 6 shots
90 min ------ ? shots
=> 90 x (6/12) = 45
Therefore, total shots fired in 90 minutes = 45 + 1 = 46 shots.
- 5. A certain job was assigned to a group of women to do it in 20 days. But 12 women did not turn up for the job and the remaining did the job in 32 days. The original number of women in the group was?
Options- A. 36
- B. 32
- C. 22
- D. 28 Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 32
Explanation:
Let the total women in the group be 'W'
Then according to the given data,
W x 20 = (W-12) x 32
=> W = 32
Therefore, the total number of women in the group = 32
- 6. One girl can eat 112 chocolates in half a minute, and her boy friend can eat half as many in twice the length of time. How many chocolates can both boy and girl eat in 12 seconds ?
Options- A. 44
- B. 32
- C. 56
- D. 49 Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 56
Explanation:
Girl eats 112 chocolates in 30 sec
so she can eat in 12 sec is 12 x 112/30 = 44.8 chocolates.
Her boy friend can eat one-half of 112 in twice of 30 sec
so he can eat 56 in 60 sec
Then he can eat in 12 sec is 56 x 12/60 = 11.2 chocolates.
Hence, together they can eat = 44.8 + 11.2 =56 chocolates in 12 seconds.
- 7. K can build a wall in 30 days. L can demolish that wall in 60 days. If K and L work on alternate days, when will the wall be completed ?
Options- A. 120 days
- B. 119 days
- C. 118 days
- D. 117 days Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 117 days
Explanation:
K's work in a day(1st day) = 1/30
L's work in a day(2nd day)= -1/60(demolishing)
hence in 2 days, combined work= 1/30 - 1/60 =1/60
since both works alternatively, K will work in odd days and L will work in even days.
1/60 unit work is done in 2 days
58/60 unit work will be done in 2 x 58 days = 116 days
Remaining work = 1-58/60 = 1/30
Next day, it will be K's turn and K will finish the remaining 1/30 work.
hence total days = 116 + 1 = 117.
- 8. Five men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work ?
Options- A. 18 days
- B. 20 days
- C. 16 days
- D. 14 days Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 20 days
Explanation:
(5m + 9w)10 = (6m + 12w)8
=> 50m + 90w = 48w + 96 w => 1m = 3w
5m + 9w = 5m + 3m = 8m
8 men can do the work in 10 days.
3m +3w = 3m + 1w = 4m
So, 4 men can do the work in (10 x 8)/4 = 20 days.
- 9. Amar can do a piece of work in 10 days. He works at it for 4 days and then Arun finishes it in 9 days. In how many days can Amar and Arun together finish the work ?
Options- A. 4 days
- B. 8 days
- C. 3 days
- D. 6 days Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 6 days
Explanation:
4/10 + 9/x = 1 => x = 15
Then both can do in
1/10 + 1/15 = 1/6 => 6 days
- 10. A, B and C can do a piece of work in 72, 48 and 36 days respectively. For first p/2 days, A & B work together and for next ((p+6))/3days all three worked together. Remaining 125/3% of work is completed by D in 10 days. If C & D worked together for p day then, what portion of work will be remained?
Options- A. 1/5
- B. 1/6
- C. 1/7
- D. 1/8 Also asked in: GATE, GRE, Analyst, Bank Clerk, Bank PO, Database Administrator, IT Trainer, AIEEE, Bank Exams, CAT
Correct Answer: 1/6
Explanation:
Total work is given by L.C.M of 72, 48, 36
Total work = 144 units
Efficieny of A = 144/72 = 2 units/day
Efficieny of B = 144/48 = 3 units/day
Efficieny of C = 144/36 = 4 units/day
According to the given data,
2 x p/2 + 3 x p/2 + 2 x (p+6)/3 + 3 x (p+6)/3 + 4 x (p+6)/3 = 144 x (100 - 125/3) x 1/100
3p + 4.5p + 2p + 3p + 4p = 84 x 3 - 54
p = 198/16.5
p = 12 days.
Now, efficency of D = (144 x 125/3 x 1/100)/10 = 6 unit/day
(C+D) in p days = (4 + 6) x 12 = 120 unit
Remained part of work = (144-120)/144 = 1/6.
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