Question

A contractor with a work force of 420 men can complete a work of construction of
a building in nine months. Due to request by the owners he was asked to complete
the job in seven months. How many extra men he must employ to complete the job?​

Answer 1

Answer:

Let a be the extra number of men employed to complete the work in 7 months.

Number of men    420      a

                                 ↓       ↓

Months                      9      7

As we know,

the number of men hired and the time required to finish the piece of work are inversely proportional.

Therefore,  

420 × 9 = a × 7

a = 540

The number of extra men required to complete the job in 7 months

= 540 - 420 = 120

Answer 2

Answer: 120

Step-by-step explanation:

Assumption :-

Work to be done be p

Also,

420 persons to complete the work time taken :-

p = 9 months

Hence,

p = 420 × 9

p = 3780

Now,

Complete the work in 9 months

$\tt{\rightarrow p=\dfrac{3780}{7}}$

p = 540

People Required :-

= 540 - 420

= 120

Hence we get,

Contractor had to employ 120 people more

Additional Information :-

→ If a person Q completes 1/c th part of work in one day, then the time taken by Q to complete the work = c days

→ If a man takes 50 days to complete a piece of work then according to the unitary method work done in a 1 day = 1/50