Question

150 workers were engaged to finish a job in a Certain number of days. 4 workers dropped number of day, 4 more workers drop on third day so on. It took 8 more days to finish the work find the number pf days in which the work was completed. Please help me ​ ​jn

Answer 1

Explanation:

$\sf \large \:\underline{ \red{Question }}:-$

150 workers were engaged to finish a job in a Certain number of days. 4 workers dropped number of day, 4 more workers drop on third day so on. It took 8 more days to finish the work find the number pf days in which the work was completed.

$\sf \large \:\underline{ \red{Given} }:-$

150 workers were engaged to finish a job in a Certain number of days.

4 workers dropped number of day.

4 more workers drop on third day so on.

$\sf \large \:\underline{ \red{To \: Find }}:-$

Find the number pf days in which the work was completed.

$\sf \large \:\underline{ \red{Solution }}:-$

$\boxed{ \sf \: sum \: of \: n \: terms \: = \frac{n}{2} ( \:2a + (n - 1) \times d) }$

∴ Total number of workers who would have worked all n days = 150 (n – 8)

$\sf \to \: n (152 - 2n) = 150 (n - 8) \\ \\ </p><p></p><p> \sf \to \: 152n - 2n^2 = 150n - 1200 \\ \\ \sf \to \: 2n^2 - 2n - 1200 = 0 \\ \\ </p><p></p><p> \sf \to \: n^2 - n - 600 = 0 \\ \\ </p><p></p><p> \sf \to \: n^2 - 25n + 24n - 600 = 0 \\ \\ </p><p></p><p> \sf \to n(n - 25) + 24 (n + 25) = 0 \\ \\ </p><p></p><p> \sf \to \: (n - 25) (n + 24) = 0 \\ \\ </p><p></p><p> \sf \to \: n - 25 = 0 \: or \: n + 24 = 0 \\ \\ \sf \to \orange{ n = 25 \: or \: n = \: - 24}\: \huge \dag\\ </p><p></p><p>$

$\sf \underline{ \red{n = 25 } \: (Number \: of \: days \: cannot \: be \: negative)}$

$\text{ \green{ \underline{{Thus, the work is completed in 25 days.}}}}$

Answer 2

let the work be complete in x days

The work should have been complete by x-8 days.

Total man-days= 150(x-8)

As four worker drop on each day

The total work days are 150,150-4, 150-8..... 150-(x-1)4

These are in arithmetic progression where

                           a1=150  d= - 4 and n=x

so total working man-days= x(2a1-4(x-1))/2

                                      = x(300-4x+4)/2

Then we have 150(x-8)=x(304-4x)/2

⇒  300x-2400= 304x-4x²

⇒  75x-600=76x-x²

⇒  x² -x -600=0

⇒ (x-25)(x+24)=0

solving we have x=25

The work was complete in 25 days.