Time and Work Problems for IBPS PO Pre, CET, SBI PO 2021, and LIC AAO 2021 at Smartkeeda

Direction : Read the following questions carefully and choose the right answer.
1
3 workers Peroola, Rahul and Prashant can complete a piece of work in 6 days. Peroola takes 15 days less than Rahul to complete the same work. Find in how many days will Prashant complete the whole work alone with 75% of his original efficiency, if Rahul can complete the work alone in 35 days?
» Explain it
A
Peroola + Rahul + Prashant = 6

Rahul = 35

Peroola = (35 – 15) = 20

Total units of work = 420

(Peroola + Rahul + Prashant)’s one day work = 70 units

Peroola’s one day work = 21 units

⇒ Rahul = 12 units

Prashant’s one day work = 70 – 33 = 37 units

Prashant’s efficiency to do the work alone

75  × 37
100

Time required to complete the work

420 × 4  =  560  days
37 × 3 37

Hence, option A is correct.
2
Three persons A , B, and C complete a piece of work in 6 days for which they are paid a sum of Rs. 480.If the efficiency of A, B and C are in ratio 4 : 5 :7, then find the daily income of B?
» Explain it
A
Total amount earned by A ,B, and C in 6 days =Rs 480

The amount earned by them in 1 day =  480  = Rs 80
6

Amount of money earned is proportional to the amount of work done

Let work done by A ,B and C be 4x, 5x and 7x.

∴ Total work done by A,B and C together= 16x

Work done by B = 5x

Daily income of B =  5x  × 80 = Rs. 25
16x

Hence, option A is correct.
3
Rashmi and Pallavi can make a carpet in 3 days and 12 days more than the time taken if both of them worked together. Find the time in which Rashmi can make the carpet alone.
» Explain it
A
Let the time both of them together will take to make the carpet be x days

Time taken by Rashmi alone = x + 3 days

Time taken by Pallavi alone = x + 12 days

One day work when they both work together = Sum of their individual per day work

1  =  1  +  1
x x + 12 x + 3

1  =  2x + 15
x x2 + 15x + 36

x2 + 15x + 36 = 2x2 + 15x

x = 6

Time taken by Rashmi to make carpet alone = 6 + 3 = 9 days

Hence, option A is correct.
4
Three workers Trump, Putin and Jinping are appointed to do a job. They together started the job but Jinping left after 3 days when 37% of the job was done. The remaining job was completed by Trump and Putin in 7 days. The ratio of efficiency of Trump and Putin is 4 : 5. Find the number of days required by the slowest worker to complete the entire job alone?
» Explain it
E
Let x, y and z are the one day’s work of Trump, Putin and Jinping respectively.

According to the question,

⇒ 3 × (x + y + z) = 37% of the work

⇒ 7 × (x + y) = 63%

⇒ x + y = 9%

∵ The ratio of efficiency of Trump and Putin is 4 : 5,

∴ 5x = 4y and x = 4%, y = 5% work per day.

It implies Trump can complete the job and in 25 days and Putin in 20 days.

In 3 days (x + y + z) do 37% of the work

Out of this Trump and Putin would do 27% work = (3 × 9%) of the work.

Remaining work = 37% – 27% = 10% (done by Jinping in 3 days)

∴ The work of z =  10  = 3.33% work per day
3

∴ Jinping is the slowest and he would do the work in 30 days.

Hence, option E is correct.
5
A group of men decided to do a job in 4 days, but 20 men dropped out everyday. Find the number of men who initially decided to do the job, if job was completed in 7 days?
» Explain it
C
Let the initial number of men be m

Total work = 4 m

m + (m – 20) + (m – 40) + …… = 4 m

7  [2m + 6 (–20)] = 4m
2

7  (2m – 120) = 4m
2

m =140

Hence, option C is correct.