Thursday, 14 April 2016

[Q] Time and Work Tricks - 2

Please read Part-1, before going through this post. In this article, I have solved questions where some workers quit in the middle, as well as some questions on efficiencies.


Note: In the complete Time and Work series, Efficiency would mean "Work Done in 1 day", and efficiency has been denoted by small letters, e.g. "a" means "Efficiency of A".


Q. 1)

If Pratibha finishes the work in X days, then Sonia will take 3X days to finish the same work
Given 3X – X = 60
Or X = 30
Pratibha takes 30 days and Sonia takes 90 days
Answer: (A)


Q. 2)


Let the total work be 24 units.
Efficiency of Sunil = 24/4 = 6 units (Since Sunil takes 4 days to complete the work)
Efficiency of Ramesh = 6 * 1.5 = 9 units (Since Ramesh is 1.5 times efficient as Sunil)
Efficiency of Dinesh = 24/6 = 4 units ((Since Sunil takes 6 days to complete the work))
Efficiency of (Sunil + Ramesh + Dinesh) = 6 + 9 + 4 = 19 units
Time required to finish the complete work = 24/19 days
Answer: (D)

Q. 3)


Let the total work be 15 units. Efficiency of A = a and Efficiency of B = b
A and B complete the work in 5 days.
Hence efficiency of A and B = 15/5 = 3 units
So, a + b = 3 … (1)
New efficiency of A = 2a
New efficiency of B = b/3
With new efficiency the work was completed in 3 days.
So, 2a + b/3 = 15/3 = 5 … (2)
Solve (1) and (2), you will get a = 12/5 = 2.4 units
So A will complete 15 units work in 15/2.4 or 25/4 days
Answer: (B)

Q. 4)

Let the total work be 24 units
Given, 3*Efficiency of A = Efficiency of B + Efficiency of C
3a = b + c
A, B and C compete the work in 24 days.
Hence, a + b + c = 24/24 = 1 or 4a = 1 [Put b + c = 3a]
a = 1/4 = 0.25 unit
A completes 0.25 unit work in 1 day. So to complete 24 units of work, he will take 24/0.25 = 96 days
Answer: (B)



Q. 5)


Let the total work be 7 units. Since they all complete the work in 7 days, so their total efficiency = 7/7 = 1 unit
Let efficiency of boy = x
Then efficiency of women = 2x
Efficiency of man = 4x
x + 2x + 4x = 1
7x = 1 or x = 1/7
The boy completes 1/7 work in 1 day, so to complete 7 units of work, he will take 49 days
Answer: (A)


Q. 6)

A does 1/2 as much work as B in 3/4 of the time. Hence A will do (1/2 + 1/2) or complete work in (3/4 + 3/4) or 1.5 times more time than B.
A = 1.5B  (where A = no. of days taken by A to finish the work and B = no. of days taken by B to finish the work)
Also A*B/(A+B) = 18
Put A = 1.5B in the above equation and solve
B = 30 days
Answer: (B)

                                       Q. 7)


Let the total work = 60 units
Efficiency of A = 60/20 = 3 units
Efficiency of B = 60/30 = 2 units
Efficiency of (A + B) = 5 units
Work done by A and B in 7 days = 5*7 = 35 units
Work left = 60 – 35 = 25 units
C completes 25 units of work in 10 days. Hence he will complete 60 units of work in 10* 60/25 = 24 days
Answer: (C)


Q. 8)

Let total work be 120 units.
Efficiency of A = 120/6 = 20 units
Efficiency of B = 120/12 = 10 units
Efficiency of C = 120/15 = 8 units
Work left = 7/8 * 120 = 105 units
Efficiency of A + B = 30 units
Hence time taken by A and B to complete 105 units of work = 105/30 = 3.5
Answer: (C)

Q. 9)


Let the total work = 80 units
Efficiency of (A + B + C) = 80/40 = 2 units
Work done by (A + B + C) in 16 days = 16 * 2 = 32 units
Remaining work = 80 – 32 = 48 units
B and C complete the remaining work (48 units) in 40 days.
Efficiency of B + C = 48/40 = 1.2 units
Efficiency of A = Efficiency of (A + B + C) - Efficiency of (B + C) = 2 – 1.2 = 0.8 unit
Time taken by A to complete the whole work = 80/0.8 = 100 days
Answer: (C)

Q. 10)

Let the total work = 360 units
Efficiency of A = 360/45 = 8 units
Efficiency of B = 360/40 = 9 units
Efficiency of A + B = 17 units
Let A left after x days, that means A and B worked together for x days. Total work done by A and B together = 17x
Then the remaining work is finished by B in 23 days. Hence work done by B alone = 23 * 9 = 207 units
So, 17x + 207 = 360
Or x = 9 days
Answer: (D)

Q. 11) 

This question appeared in SSC Tier-2 2015, and stumped many candidates. Although there is nothing tricky about it. 
Let the total work be 60 units.
p + q = 60/6 = 10
q + r = 60*7/60 = 7
Given, Total work done = 3 days work of P + 6 days work of Q and R
60 = 3*p + 6*(7)
p = 6
Hence time taken by P to complete the work = 60/6 = 10 days
p + q = 10, hence q = 4
q + r = 7, hence r = 3
Hence time taken by R to complete the work = 60/3 = 20 days
Difference = 20 - 10 = 10 days
Answer : (C)

Q. 12)  4 Men and 6 Women working together can complete the work in 10 days. 3 men and 7 women working together will complete the same work in 8 days. In how many days 10 women will complete this work?

One day work for a man = 1/m
One day work for a woman = 1/w
In one day, 4 men and 6 women will do 1/10 of the work. Hence,
4/m + 6/w = 1/10    ...  (i)
Similarly,
3/m + 7/w = 1/8      ...  (ii)
Multiply equation (i) with 3 and equation (ii) with 4
12/m + 18/w = 3/10
12/m + 28/w = 1/2
Subtract the equations
10/w = 1/5
So 10 women will complete the work in 5 days
Answer: (5)


If you have any doubt in this article, please drop a comment...
Keep reading :)

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51 comments:

  1. Sir
    Aaj ke AMAR UJALA me nikla h ki ssc ka pre qualifyinh hoga aur mains online hoga aur usipe merit bnegi.

    Aapki kya report h?

    ReplyDelete
    Replies
    1. iss saal koi change nai hoga, so don't worry

      Delete
  2. http://m.dailyhunt.in/news/india/hindi/amar-ujala-epaper-amar/sijiel2016-ka-pariksha-paitarn-badala-newsid-52031476

    ReplyDelete
  3. Sir, What should be my strategy in these last 20 days to maximize my score in tier-1? It is a common question. Please write a post if possible.

    ReplyDelete
  4. Sir pls tell by efficiency method:-
    Two pipes can fill a cistern separately in 24 min and 40 min respectively. A waste pipe can drain off 30 litres per minute. If all the three pipes are opened the cistern fills in one hour. The capacity of Cistern is?

    ReplyDelete
    Replies
    1. You wont be able to solve this question with efficiency method because waste pipe ki efficiency absolute terms me di hai (30 litres).
      Let the capacity be X
      In 1 minute, the first pipe adds X/24 litres
      In 1 minute, the second pipe adds X/40 litres
      In 1 minute, the third pipe drains off 30 litres
      So in 1 minute, all the three pipes are adding (X/24 + X/40 - 30) litres.In 60 minutes, all the three pipes will add 60*(X/24 + X/40 - 30) litres. Hence
      X = 60*(X/24 + X/40 - 30)
      X = 600 litres

      Delete
    2. i don't know what is efficiency method but a simple way to solve it is- since all the pipes are opened for 60 min
      (1 hr) that means 60/24 + 60/40 -60/C = 1
      solving it will give c=20. if C operates for 20 min then it'll fill 20*30 = 600 litres [C empties 30 litres per min)

      Delete
  5. I am yamuna new to ssc exam. Iam preparing last year papers and some shortcuts from your blog.
    Is it enough to pass in tier-1?
    Please tell me the strategy that I have to follow for these 20 days?

    ReplyDelete
  6. No answer is 600 waiting for sir to reply

    ReplyDelete
  7. This comment has been removed by the author.

    ReplyDelete
  8. In ques 7 sir, we considered 20 and 30 only for lcm right? Because the othef two members are leaving and joining in btwn?

    ReplyDelete
    Replies
    1. yes...jiska jiska complete work diya ho, usi ka LCM nikalna hai

      Delete
  9. In ques 7 sir, we considered 20 and 30 only for lcm right? Because the othef two numbers are about leaving and joining in btwn?

    ReplyDelete
  10. Sir pls explain q.no 6 in detail.why take 3/4+3/4 I can't understand

    ReplyDelete
  11. Hello Sir,

    Q.9...total work 80 units..how??...it is just an assumption or any logic behind it?

    Looking forward for your reply:)

    ReplyDelete
    Replies
    1. Oops..yeah..got it...thank you so much for the response:)

      Delete
  12. why you have taken 42 units in last question...? Any logic behind this?

    ReplyDelete
    Replies
    1. No logic...take whatever you want...

      Delete
  13. Sir plzz post some more tricks for trignometry & algebra using option

    ReplyDelete
  14. sir Q.6 me i think answer is 45
    because 3/4B = 1/2A diya hai
    to A=1.5B aayega
    aur A+B=1 hai to A ki value put karne ke baad
    B=1/1.5 aa raha hai to B=45 aayega na?
    please explain

    ReplyDelete
    Replies
    1. nai yar...b=30 hi aayega...farzi me confuse kar diya tumne :D

      Delete
    2. Arey bhai..... A+B=1
      Then A=1.5B
      Put the value 1.5B+B=1
      2.5B=1
      B=1/2.5

      Delete
    3. r u sure answer is 30 :D please explain
      if not then please update the answer

      Delete
    4. agar main sure na hota to ye question post hi nai karta...how come you are getting A + B = 1
      I mean logic kya hai iss equation ka??
      Moreover, B ki efficiency A ki efficiency se jyada hai. So ye obvious hai ki B will take less time than A

      Delete
  15. Sir! How many questions are generally asked in Tier-I Work ?

    ReplyDelete
  16. Sir can u explain about question 6… how do u get complete work as 3/4+3/4

    ReplyDelete
    Replies
    1. 3/4 + 3/4 is not the complete work
      Let B perform W amount of work in T time. Then A will perform W/2 work in 3/4T time. So to perform W work, A will need 3/4T + 3/4T or 1.5T time. Hence,
      A = 1.5B

      Delete
  17. Sir...in q.4...how did u comprehend 3a=b+c??

    ReplyDelete
    Replies
    1. A takes three times as long as B and C together to complete the work. That means the efficiency of A is three times less than B and C together
      a = (b + c)/3
      3a = b + c

      Delete
  18. One more thing sir...a lot of cumbersome chit-chats are prevailing out there abt cgl pattern change n ol....it sucks our concentration immensely...plss provide some lucid explanation on that..so that we can replenish our concentration...pls sir..all messed up!!huh

    ReplyDelete
  19. In q.6...where is given 3/4th time more than B...den lastly,how can it be said 1.5times more than B??

    ReplyDelete
    Replies
    1. 3/4th more time is for 1/2 work. For complete work, the time will be 3/4+3/4 or 1.5 times more

      Delete
  20. Sir in q.8..whether it is asked to calculate total time taken or time taken for the work remaining...is not clear...should it be decided on the basis of options given??

    ReplyDelete
    Replies
    1. Yes...it is not clear...will have to go according to the options only

      Delete
  21. 4 Men and 6 Women working together can
    complete the work in 10 days. 3 men and 7
    women working together will complete the
    same work in 8 days. In how many days 10
    women will complete this work?
    (A) 8 (B) 7
    (C) 5 (D) 4
    Please solve this.

    ReplyDelete
    Replies
    1. 4/m + 6/w = 1/10
      3/m + 7/w = 1/8
      multiply equation (i) with 3 and equation (ii) with 4
      12/m + 18/w = 3/10
      12/m + 28/w = 1/2
      subtract the equations
      10/w = 1/5
      So 10 women will complete the work in 5 days

      Delete
    2. Sir even I got this answer but I used below method
      (4M+6W) *10 = (3M+7W)*8
      40M+60W = 24M +56W
      16M = -4W
      -1W = 4M
      M/W = -1/4
      Total work = 200
      10 women will complete in 200/40 = 5 days.

      In this case men's efficiency comes -1. So is the question wrong? Because if they have asked like this "In how many days 10 men will complete this work?", then what should be the approach.

      Delete
    3. yes...no of days for men will come negative. Thats why they have asked about women it seems...\your approach is fine, so you shudn't worry about it.

      Delete
  22. sir, i use this method to solve but i am not getting the ans
    10(4M +6W) = 8(3M + 7W). Please help.

    ReplyDelete
  23. Eff of 4M + 3W = 80/10 & eff of 3M +7W= 80/8 , now solve both eq. Eff. Of 10W =16 so they will work in 80/16 =5 days .. Ryt sir ?

    ReplyDelete
  24. Sir,
    I have a doubt on your post [Q] Time and Work Tricks - 2 on question 2 that,

    Suppose I take work as 12 unit s as lcm of 4 & 6 then answer comes as option 1 but you have taken 24 unit work and your ans is D.

    So, can u explain which one is right and which concept to follows?

    Thanks,
    Pawan

    ReplyDelete
  25. SOLUTION PLS -

    A and B together can finish a work in 15 days . A and C take 2 days more to complete the same work than that of B and C. B and C complete the work in 8 days . In how many days will A finish it separately ?

    options - 1) 40 d 2)24d 3) 20 4)17+1/7

    ReplyDelete
  26. Bhai 48 days is the right answer. Not there in the option. Either check ur option or question

    ReplyDelete
  27. Bhai 48 days is the right answer. Not there in the option. Either check ur option or question

    ReplyDelete