Time and Work problems
- 1. At Arihant Prakasham every book goes hrough 3 phases (or stages) typing, composing and binding. There are 16 typists, 10 composers and 15 binders. A typist can type 8 books in each hour, a composer can compose 12 books in each hour and a binder can bind 12 books in each hour. All of the people at Arihant Prakasham works for 10 hours a day and each person is trained to do only the ob of 1 category.How many books can be prepared in each day?
Options- A. 1500
- B. 1200
- C. 1440
- D. 1380 Discuss
Correct Answer: 1200
Explanation:
T C B
16 10 15
8 12 12
128 120 180 <------- in one hour
1280 1200 1800 <------- in 10 hours
Since, restriction is imposed by composers i.e,since only 1200 books can be composed i 10 hours so not more than 1200 books can be finally pepared.
- 2. K can finish the work in 18 days and L can do the same work in 15 days. L worked for 10 days and left the job. In how many days, K alone can finish the remaining work ?
Options- A. 5.5 days
- B. 6 days
- C. 4.2 days
- D. 5 days Also asked in: GATE, CAT, Bank Exams, Bank PO, Bank Clerk
Correct Answer: 6 days
Explanation:
L's 10 days work =
Remaining work =
Now, work is done by K in one day = 1/18
1/3 work is done by K in = 6 days
- 3. A constructor estimates that 4 people can paint Mr. Karthik's house in 6 days. If he uses 5 people instead of 4, how long will they take to complete the job ?
Options- A. 3 days
- B. 26/3 days
- C. 13/4 days
- D. 24/5 days Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Analyst, Bank Clerk, Bank PO
Correct Answer: 24/5 days
Explanation:
we know that m1 x d1 = m2 x d2
=> 4 x 6 = 5 x d
where d = no. of days taken by 5 men to paint
d = 24/5 days.
- 4. Two boys and a girl can do a work in 5 days, while a boy and 2 girls can do it in 6 days. If the boy is paid at the rate of 28$ a week, what should be the wages of the girl a week ?
Options- A. 24 $
- B. 22 $
- C. 16 $
- D. 14 $ Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 16 $
Explanation:
Let the 1 day work of a boy=b and a girl=g, then
2b + g = 1/5 ---(i) and
b + 2g = 1/6 ---(ii)
On solving (i) & (ii), b=7/90, g=2/45
As payment of work will be in proportion to capacity of work and a boy is paid $ 28/week,
so a girl will be paid
= 16 $.
- 5. A can do a work in 9 days, B can do a work in 7 days, C can do a work in 5 days. A works on the first day, B works on the second day and C on the third day respectively that is they work on alternate days. When will they finish the work ?
Options- A. [7 + (215/345)] days
- B. [6 + (11/215)] days
- C. [6 + (261/315)] days
- D. [5 + (112/351)] days Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: [6 + (261/315)] days
Explanation:
After day 1, A finishes 1/9 of the work.
After day 2, B finishes 1/7 more of the total work. (1/9) + (1/7) is finished.
After day 3, C finishes 1/5 more of total work. Total finished is 143/315.
So, after day 6, total work finished is 286/315.
Now remaining work = 29 /315
On day 7, A will work again
Work will be completed on day 7 when A is working. He must finish 29/315 of total remaining work.
Since he takes 9 days to finish the total task, he will need 261/315 of the day.
Total days required is 6 + (261/315) days.
- 6. A group of men can complete a job in K hours. After every 4 hours, half the number of men working at that point of time leave the job. Continuing this way if the job is finished in 16 hours, what is the value of K ?
Options- A. 7 hrs
- B. 7.5 hrs
- C. 8 hrs
- D. 8.25 hrs Also asked in: TOEFL, GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 7.5 hrs
Explanation:
Let there are L men
job requires LK man hours.
job completed in first 4 hrs = L x 4 = 4L
job completed in next 4 hrs = 4 x L/2 = 2L
job completed in next 4 hrs = 4 x L/4 = L
job completed in last 4 hrs = 4 x L/8 = L/2
4L + 2L + L + L/2 = KL
K = 7+1/2 = 7.5 hours.
- 7. P and Q were assigned to do a work for an amount of 1200. P alone can do it in 15 days while Q can do it in 12 days. With the help of R they finish the work in 6 days. Find the share of R ?
Options- A. 120
- B. 240
- C. 360
- D. 180 Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 120
Explanation:
1/15 + 1/12 + 1/R = 1/6, we got R = 60 (it means R will take 60 days to complete the work alone)
so ratio of work done by P:Q:R = 1/15 : 1/12 : 1/60 = 5 : 4 : 1
so R share = (1/10) x 1200 = 120.
- 8. If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time ?
Options- A. 1:2
- B. 1:3
- C. 3:1
- D. 2:1 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 2:1
Explanation:
5M + 2B = 4(1M + 1B)
5M + 2B = 4M + 4B
1M = 2B
The required ratio of work done by a man and a boy = 2:1
- 9. 45 men working 9 hours per day dig 40 m deep. How many extra men should be put to dig to a depth of 56 m working 7 hours per day ?
Options- A. 36
- B. 61
- C. 48
- D. 54 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 36
Explanation:
(45 x 9)/40 = (M x 7)/56 => M = 81
=> 81 ? 45 = 36
- 10. If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day ?
Options- A. 101 men
- B. 112 men
- C. 102 men
- D. 120 men Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 102 men
Explanation:
From the above formula i.e (m1 x t1/w1) = (m2 x t2/w2)
so, [(34 x 8 x 9)/(2/5)] = [(M x 6 x 9)/(3/5)]
so, M = 136 men
Number of men to be added to finish the work = 136-34 = 102 men.
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