Question

your work is completed by some workers in some days if the number of workers exceeds by 25 the work completes 5 days earlier if the number of workers is less by 50 then it takes 20 more complete the work then find the number of workers and days taken by them to complete that work​

Answer 1

Answer:

Number of days taken to complete the work is 10 days

Number of men needed to complete the work is 75 .

Step-by-step explanation:

Given as:

Number of worker = m

number of days = d

if the number of workers exceeds by 25 the work completes 5 days earlier

So, new worker = m + 25

And new days = d - 5

Now,

$\dfrac{men\times days}{work}$  = constant

So ,$\dfrac{m_1\times d_1}{w_1}$  =  $\dfrac{m_2\times d_2}{w_2}$

or, m × d = ( m + 25 ) × ( d - 5 )

or, m d = m d - 5 m + 25 d - 125

Or, - 5 m + 25 d = 125              .........1

Again

if the number of workers is less by 50 then it takes 20 more days to complete the work

So, Similarly

m × d = ( m -50 ) × ( d + 20 )

Or, m d = m d + 20 m - 50 d - 1000

Or, 20 m - 50 d = 1000                ........2

Solving eq 1 and 2

(  20 m - 50 d ) + 4 × (  - 5 m + 25 ) = 1000 - 4 × 125

Or, ( 20 m - 20 m) + ( - 50 d + 100 d) = 500

or, 0 + 50 d = 500

∴      d = $\dfrac{500}{50}$

i.e d = 10

So, Number of days taken to complete the work = d = 10 days

Put the value of d in 2

20 m - 50 × 10 = 1000  

Or, 20 m = 1000 + 500

∴    m = $\dfrac{1500}{20}$

i.e  m = 75

So, Number of men needed to complete the work = m = 75

Hence, Number of days taken to complete the work is 10 days

And Number of men needed to complete the work is 75 . Answer