| Day |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
| Person |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
${\color{Blue} F}$ |
${\color{Red} C}$ |
| Work done (in units) |
1 |
4 |
3 |
4 |
5 |
4 |
7 |
4 |
9 |
4 |
11 |
4 |
13 |
4 |
15 |
4 |
17 |
4 |
19 |
4 |
21 |
4 |
23 |
4 |
25 |
The ratio of work done by $Chandan$ on $1^{st}$ day to done by $Falguni$ on $2^{nd}$ day=$1:4$
Let $Chandan$(${\color{Red} C}$) does $1$ unit of work on $1^{st}$ day and $Falguni$(${\color{Blue} F}$) does $4$ units of work on $2^{nd}$ day
$\because$ $Falguni$ does a constant amount of work everyday so she will work $4$ units on every alternate day
$\Rightarrow$ Total work done by $Falguni$ = $4+4+4...12$ times $= 4*12 = 48$ units
$\because$ $Chandan$ does $d$ amount of work on $d$ day so he will do different units of work every alternate day
$\Rightarrow$ Total work done by $Chandan$ = $1+3+5+7...25$ = $\frac{13}{2}(1+25) = 13 *13 = 169$ ( $\because$ sum of a.p. = $\frac{n}{2}(a+l)$)
So total work done by $Falguni$ and $Chandan$ in $25$ days = $48+169$ =$217$ units.
Question is asking that in how many days will $Falguni$ be able to do $217$ units of work if she does $4$ units of work everyday
$\therefore$ Days required by $Falguni$ to complete the work alone = $\frac{217}{4}$ = $54\tfrac{1}{4}$ = 54.25 days
