QUESTIONS ON TIME & WORK (PART-IV)

QUERY 31

Two workers A and B working together completed job in 5 days. Had A worked twice as efficiently as he actually did and B worked 1/3 as he actually did, the work would have been completed in 3 days. A alone could complete the work in?

A) 6.15 days
B) 6.25 days
C) 7.5 days
D) 8 days

MAHA GUPTA
Let A alone can do the whole in x days and B alone can do it in y days

CASE-I
Now A’s 1 day work = 1/x
And B’s 1 day work = 1/y
(A + B)’s 1 day work = 1/5

Therefore 1/x + 1/y = 1/5 —-(i)

CASE-II (Had A worked twice as efficiently as he actually did and B worked 1/3 as he actually did)

A’s 1 day work = 2/x
B’s 1 day work = 1/3y
(A + B)’s 1 day work = 1/3

Therefore 2/x + 1/3y = 1/3 —-(ii)

Solving equations (i) and (ii)
x = 6.25

Therefore A alone can do the work in 6.25 days (option ‘B’)

QUERY 32

A is twice as good as  B and B takes 12 more days to do a work. In how many days both will complete the work?

A) 10 days
B) 8 days
C) 9 days
D) 6 days

MAHA GUPTA
A is twice as good a workman as B, means if A does a piece of work in 1 day then B does it in 2 days. We see the difference is between them is 1 day.

So, if the difference is 1 day, A does the work in 1 day and B does it in 2 days
If difference is 12 days A will do it in 1*12 i.e. 12 days and B will do it in 2*12 i.e. 24 days

Thus, A’s 1 day work = 1/12
And B’s 1 day work = 1/24
And (A + B)’s 1 day work = 1/12 + 1/24 = 3/24 = 1/8

Therefore the number of days in which both working together will do that work = 8 days (option ‘B’)

QUERY 33

A and B together complete a job in 8 days. Both B and C working alone can finish the same job in 12 days. A and B commence on the job and work for 4 days whereupon A leaves. B continue for 2 more days and leaves too. Now C start working and finish the job. How many days C require?

A) 3
B) 4
C) 5
D) 8

MAHA GUPTA
(A + B)’s 1 day work = 1/8
B’s 1 day work = 1/12
C’s 1 day work = 1/12

So work finished = (A + B)’s 4 day work + B’s 2 day work
= (1/8)4 + (1/12)2 = ½ + 1/6 = 4/6 = 2/3

Remaining work = 1 – 2/3 = 1/3

Time taken by C to do 1/12 of work = 1 day
Therefore time taken by him to do 1/3 of work = 12*(1/3) = 4 days (option ‘B’)

QUERY 34

If 8 men or 12 women do a piece of work in 25 days. In how many days same work will be done by 6 men and 11 women?

A) 10 days
B) 12 days
C) 15 days
D) none

MAHA GUPTA
Either convert men into women or women into men, let’s do the former

8 men = 12 women
Therefore 6 men = (12/8)*6 = 9 women

Thus 6 men + 11 women = 9 women + 11 women = 20 women

Now time taken by 12 women = 25 days
Hence time to be taken by 20 women = (25*12)/20 = 15 days (option ‘C’)

QUERY 35

Wages for 45 women is Rs 15,525 in 48 days. How many men must work for 16 days to receive Rs 5,750; daily wages of a man being double of a woman.

A) 20 days
B) 18 days
C) 25 days
D) 22 days

MAHA GUPTA
As we have to find number of men for 16 days, so find wages of women for 16 days also so that comparison could me made

Now 16 days’s wages of 45 women = (15,525/48)16 = 5,175
Therefore number of women to earn 5,750 in 16 days = (45/5175)5750 = 50 women

But wages of a man is double of a woman, therefore, number of men must be working = 50/2 = 25 (option ‘C’)