# Working in Group Using Time and Work Formula (03)

In this post we will cover Time and Work Questions that involve people working in groups.

Each chapter in quantitative aptitude has different category of questions. We as a student should focus on understanding each category and find out ways to solve the problems as fast as possible.

Most of the below questions can be easily solved using Time and Work Formula, so make sure you remember it for your competitive exams.

(01) A certain number of men can complete a job in 30 days. If there were 5 men more, it could be completed in 10 days less. How many men were in the beginning?

Let initially the number of men be x.
So x men complete the work in 30 days

Now if 5 more men are added then the work get completed in 20 days

Acc to question-

M1 D1 W2 = M2 D2 W1

x × 30 = ( x + 5 ) × ( 30 – 10 )

x = 10

Hence there are 10 men in the beginning

(02) A contractor undertakes to make a road in 40 days and employs 25 men. After 24 days, he finds that only one – third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier?

Number of Men = 25
Work completed in 24 days = 1/3

Need to find extra men that can complete the work left
Work left =(1-1/3) =2/3

Want to complete work 4 days earlier = 40-4 = 36 days
Days left = 36 – 24 = 12

Using Time and Work formula for Quantitative aptitude

25 × 24 / 1/3 = ( 25 + x ) × 12 / 2/3 of ( 1 – 1/3 )

x = 75

Hence 75 extra men is needed to complete the work in that required time frame

(03) 8 men working for 9 hours a day complete a piece of work in 20 days. In how many days can 7 men working for 10 hours a day complete the same piece of work?

8 Men –> 9 Hours –> 20 days
Total unit of work done => 8 * 9 * 20 => 1440 units

Now there are 7 men working for 10 hours
How many days to complete the same work?

Hence it will take 20 * (4/7) days to complete the same piece of work

(04) If 72 men can build a wall of 280 m length in 21 days, how many men could take 18 days to build a similar type of wall of length 100 m?

Men 1 = 72
Days 1 = 21
Work 1 = 280 m wall

Days 2= 18
Work 2 = 100 m wall
Men 2 =?
Find the number of men

Using Time and Work Formula

Hence 30 men are needed to build 100 m wall in 18 days

(05) A road of 5 km length will be constructed in 100 days. So 280 workers were employed. But after 80 days it was found that only 3.5 km road was completed. No how many more people were need to finish the work in the specified time?

Let ‘n’ more number of men are required to complete the job in 20 days.

Men 1= 280 Workers
Days = 80

Men 2= 280 + x
Days left = 20 This question can be easily solved using Time and Work formula

The above equation can be easily solved
280 + n = 480
n = 200

Hence we need 200 more workers to complete the work in stipulated time

(06) Some carpenters promised to do a job in 9 days but 5 of them were absent and remaining men did the job in 12 days. The original number of carpenters was?

Original Number of Carpenters = n
Time Promised = 9 days

Number of Carpenters Present =x-5
Time Taken = 12 days

Using Time and Work Formula

On solving the equation we get

4n – 20 = 3n

n = 20

Hence there original number of carpenters = 20