Time par Work - Himanshi Ahuja
Content Developer, Genius Tutorials | Maths ( Hons.) from Sri Venkateshwar College, Delhi University | CAT 2016 QA - 98.8 Percentile
Q1) Rahul and Anjali can complete a piece of work in 16 days , which Anjali can complete in 32 days . If Rahul and Anjali work on alternate days , starting with Anjali , in how much time would the work be completed ?
b) 17.66 days
c) 20 days
d) 32 days
METHOD 1 :
let the work be 32 units
R + A ( in 1 day ) = 2 units
A ( in 1 day ) = 1 unit
=> R ( in 1 day ) = 1 unit
work will be completed in 32/(1+1) = 16 shifts
days = 16 * 2 = 32
METHOD 2 : rahul completes in x days
16 * x/(16+x) = 32
x = 32
rahul completes in 32 days
anjali in 32 days
both working alternately do 1/32 +1/32 = 1/16 work in 1 shift i.e. 2 days
work will be completed in 16 shifts
i.e. 32 days
Q2) 64 men working 8 hour a day plan to complete a piece of work in 9 days . However , 5 days later they found that they had completed only 40% of the work. They now wanted to finish the remaining portion of the work in 4 more days. How many hours per day should they need to work in order to achieve the target ?
apply the formula (M1 * D1 * T1)/W1 = (M2 * D2 * T2)/W2
let no. of hours be t
(64 * 8 * 5)/(2/5) = (64 * x * 4)/(3/5)
Q3) Ayush can do a piece of work in a certain number of days. To do the same piece of work , Bhavna takes thrice the number of days as Ayush takes whereas Charu takes thrice as many days as Bhavna does and Dhanush takes thrice as many days as Charu does . Now they are paired and two groups are formed. The first pair takes one – third the time taken by the second pair to complete the work. Which is the first pair ?
a) Ayush and Dhanush
b) Ayush and Charu
c) Charu and bhavna
d) Bhavna and Dhanush
A = 1
B = 3
D = 27
now , either by options or by thoda sa idea
AC takes 1/3 rd time taken by BD .
Q4) Consider three friends A, B and C who work at differing speeds. When the slowest two work together they take n days to finish a task. When the quickest two work together they take m days to finish a task. One of them, if he worked alone would take thrice as much time as it would take when all three work together. How much time would it take if all three worked together?
Let A < B < C days.
now B takes thrice as much as A,B,C together.
so 3/B= (1/A+1/B+1/C) --(1)
1/n = 1/B+1/C and 1/m = 1/A+1/B
1/n+1/m-1/B = 1/A+1/B+1/C = 3/B= work by all 3 in one day
so 1/n+1/m = 4/B
so B= 4mn/(m+n) so from (1), days reqd by all three= 4mn/3(m+n)
Q5) Jai and Ram can complete a piece of work in 12 and 24 days respectively. Jai started the work and after a few days Ram joined him and the work was complete in 10 days. After how many days did Ram join Jai ?
Let total work be 24 units
J = 2 units
R = 1 unit
J does 20 units
R = 4 units
4 units in 4 days
Hence after 6 days
Q6) A can do a work in 4 days. Efficiency of B is half the efficiency of A, efficiency of C is half the efficiency of B and efficiency of D is half the efficiency of C. after they have been grouped in two pairs it is found that the total number of days taken by one group is (2/3)^𝑟𝑑 the time taken by the other group . Which of the following is a possible group ?
Let work be 32 units
A = 4 DAYS => 8 units
B = 8 DAYS => 4 units
C = 16 DAYS => 2 units
D = 32 DAYS => 1 unit
BC = 6 UNITS
AD = 9 UNITS
which is 2/3 rd
Q7) Albela, Bob and Chulbul have to read a document of seventy eight pages and make a presentation next day Albela can read a page in 2 minutes, Bob in 3 minutes, and Chulbul in 4 minutes. If they divide the article into 3 parts so that all three of them spend the equal amount of time on the article, the number of pages that Bob should read is ( XAT 2013 )
A : B : C = 6 : 4 : 3
so , 4/13 * 78 = 24
Q8) Aman, Baman and Chaman can finish a job working alone in 15, 20 and 25 days respectively.However, while working with somebody the efficiency of Aman, Baman and Chaman reduces by 30%, 20% and 50% respectively. If none of them is allowed to work for three consecutive days, then what is the maximum possible fraction of the job that they can complete in four days?
Let the job be of L.C.M.(15, 20, 25) = 300 units.
The number of units completed by Aman, Baman and Chaman in a day while working alone on the job are
20, 15 and 12 respectively.
The number of units completed by Aman, Baman and Chaman in a day while working on the job with
somebody else are 14, 12 and 6 respectively.
Aman, Baman and Chaman together complete 14 + 12 + 6 = 32 units of work in a day.
The number of units completed will be 32 + 20 + 18 + 32 = 102.
hence 102/300 = 17/50
Q9) One man and six women working together can do a job in 10 days. The same job is done by two men in ‘𝑝’ days and by eight women in 𝑝+5 days. By what percentage is the efficiency of a man greater than that of a woman?
let : men does m units
women does w units
total work = 10 (m+6w)
so, 10(m+6w) / 8w - 10(m+6w)/2m = 5
5/4 (m/w) - 30 (w/m) = 5/2
m/w = 6
so m = 6w
efficiency : (6w - w)/w * 100
= 500 %
Q10) The work done by 2 men in a day is equal to the work done by 3 children in a day. The work done by 3 men in a day is equal to the work done by 5 women in a day. It takes 10 days for a man, a woman and a child to complete a job working together. How many days will 2 children working together take to complete the same job?
TW=10 * 34=340
Two children will take 340/(10 * 2) = 17