Question

To complete a task two men work on first day and three men work on second day and so on ,till it gets completed.If the same work can be completed by 9 mens for 15 days,in how many days will the work

Answer 1

Answer:

15days

since, work of 9 men in 1 day => 9m=1/15

so, work of 1 man in 1 day => m=1/9*15

According to Question...

2*(1/9*15) + 3*(1/9*15) + 4*(1/9*15)+....+ upto nth term = 1 {total work}

=> 2 + 3 + 4 +.....+ upto nth term = 9*15

=>9*15 = n/2 (2*2 + (n-1)*d) {finding out the value of n(total days) by sum of nos. in A.P}

=>n^2+3n-270=0

=>(n+18)(n-15)=0

So, n=15days.

Answer 2

Answer:

Total number of days = 15 days .

Step by step solution :

Work done by 9 men in 15 days will be = 15 × 9

                                                                  = 135 units.

According to question ,

on first day work will be done by = 2men

on second day work will be done by = 3 men

similarly on 3rd day 4 men will work on so ..

all the work done by these men is same as 9 men

∴ 2×1 +3×1+4×1+.......n = 135

adding 1 on both sides

1+2+3+4......n=135

n×$\frac{n + 1}{2}$ = 135

using mid term splitting method..

$n^{2} + n- 272 = 0$

$n^{2} + 17n - 16n - 272 = 0$

n= 16

As two person work on first day and 16 on the last day , total number of days is 15 .

Learn more about arithmetic progression:

https://brainly.in/question/38598682

learn how to solve A.P:

https://brainly.in/question/36223374

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