Question

A group of men was employed to shift 545 crates. Every day after the first, 6 more men than the
previous day were put on the job. Also, every day after the first, each man working, shifted 5 fewer
crates than the number of crates moved by each man the previous day. 5 days were required to finish
the work. What was the number of men working on the fifth day?​

Answer 1

Answer:

Plz can you provide the options !!!!

Answer 2

Concept

Number total crates shifted on any day = number of men working on that day $\times$ crate shifted by each man on that day.

Given

Total number of crates to be shifted$=545$, $6$ more men were used on each day and $5$ less crates were shifted than the previous day

To find

Number of men working on the fifth day

Solution

Let number of men employed on first day$=x$

and the number of crates shifted on first day by each men$=y$

So total number of crates shifted on first day$=xy$

On second ay total number of crates shifted$=(x+6)(y-5)$  etc.

For five days the equation can be formed as

$xy+(x+6)(y-5)+(x+12)(y-10)+(x+18)(y-15)+(x+24)(y-20)=545\\\Rightarrow xy+xy-5x+6y-30+xy-10x+12y-120+xy-15x+18y-270+xy-20x+24y-480=545\\\Rightarrow 5xy-50x+60y-900=545\\\Rightarrow x=\dfrac{289-12y}{y-10} .... (1)$

Now on the fifth day $y-20$ is there , so $y$ can not be less than $20$

So possible values of $y=21,22,23,....$

But $x=$number of men should be integer value , for $y=21,22$ $x$ is not integer.

On putting $y=23$ in $(1)$ ,$x=1$

Therefore, $x=1, y=23$

On the fifth day number of men

$=x+24\\=1+24\\=25$

As a result, number of men on fifth day is $25$