Quants 24 - Time and Work

Practice Questions:

Question 1:

Sakshi can do a piece of work in 20 days. Ziva is 25% more efficient than Sakshi. The number of days taken by Ziva to do the same piece of work is:

Ratio of times taken by Sakshi and Ziva is 125:100 = 5:4
Suppose Ziva takes x days to do the work,
5 : 4 :: 20 : x => x = (4 * 20) / 5 = 80/5 = 16 days.
Hence, Ziva takes 16 days to complete the work.

Question 2:

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could do in 23 days?

Ratio of times taken by A and B = 100:130 = 10:13
Suppose B takes x days to do the work,
Then 10 : 13 :: 23 : x => x = (23 * 13) / 10 = 299/10
A's 1 day work = 1/23; B's 1 day work = 10/299
A+B 's 1 day work = 1/23 + 10/299 = 23/299 = 1/13
A and B together can complete the work in 13 days.

Question3:

A does half as much as B in three-fourth of the time. If together, they take 18 days to complete the work, how much time shall B take to do it?

Suppose B takes x days to complete the work,
A takes 2*(3/4)x = 3/2 x days
A+B 's 1 day work = 1/18
1/x + 2/3x = 1/18
x = 36/5 days.

Question 4:

A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 40 days, then A, B and C together can do the work in:

A's 1 day work : B's 1 days work = 150 : 100 = 3 : 2
Let A's and B's 1 day work be 3x and 2x respectively.
Then C's 1 day work = (3x+2x)/2 = 5x/2
5x/2 = 1/40 => 5x = 1/20 => 100x = 1
x= 1/100
A's 1 day work = 3/100
B's 1 day work = 2/100 = 1/50
C's 1 day work = 5/100 / 2 = 5/200 = 1/40
A+B+C 's 1 day work = 3/100 + 2/100 + 5/200 = 15/200 = 3/40
So, A, B and C can complete the work in 40/3 = 13 1/3 days.

Question 5:

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

Let A's 1 day work = x
Let B's 1 day work = y
Then x+y = 1/5 and 2x + 1/3y = 1/3
Solving the above 2 equations,
x = 4/25 and y = 1/25
A's 1 day work = 4/25
So, A alone could complete the work in 25/4 = 6 1/4 days.

Time to Think:

A can do a work in 15 days and B in 20 days. If they work together for 4 days, then the fraction of the work left is: