Q] A 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 days more to complete that work. Then find the number of workers and days taken by them to complete that work.
Let the number of workers be x and
the days to complete the work be y.
Sol:
Total work done
(x + 25)
∴
∴
As per the 1st condition
(y – 5)
=
xy
xy
∴
25y
–
125
–
5x
+
=
xy
∴
–
x
5y
+
=
25
……(i)
As per the second condition
(x –50)
∴
(y + 20)
=
xy
xy
∴
50y
–
1000
+
20x
–
=
xy
∴
20x
50y
–
=
1000
……(ii)
∴
2x
5y
–
=
100
What do we need to find?
No. of workers | No. of days | Work done |
| | |
| | |
| | |
2
5
2 × 5 = 10
3
6
3 × 6 = 18
x
y
x × y = xy
Let us take an example
If 2 workers work for 5 days
Total work done will be
If 3 workers work for 6 days
Total work done will be
Similarly If x workers work for y days
Total work done will be
∴
25y
=
–5x
+
125
(dividing throughout by 5)
(dividing throughout by 10)
Here y has the same coefficient with different signs
Here y has the same coefficient with different signs
So let us add the two equations
If the number of workers exceeds by 25 means the new number of workers
= x + 25
Work gets completed 5 days earlier means number of days to required to complete the work = y - 5
Did the total work change??
No, it is a same and the total work done = xy
= xy
Adding equations (i) and (ii)
–
x
5y
+
=
25
2x
5y
–
=
100
x
=
125
Substituting x = 125 in equation (ii)
125
–
+
5y
5y
25
=
+
125
∴
∴
=
25
5y
150
=
∴
y
30
=
∴
Substitute the value of x in any of the two equations
The number of workers is 125
and the number of days to
complete the work is 30.