Problems based on Work Done
3 women and 6 men can finish it in 3 days.
Find the time taken by 1 woman alone to finish the work and also that taken by 1 man alone.
Soln.
Let the no. of days a woman takes to complete the work alone be x
& that a man would take be y.
∴ Work done by 1 woman in one day
1
x
=
∴ Work done by 1 man in one day
1
y
=
According to the first condition
2
x
+
5
y
=
1
4
According to the second condition
3
x
+
6
y
=
1
3
Work | No. of days required to finish the work | Work done one day |
| | |
| | |
| | |
What we need to
find ?
1
2
1
3
1
x
Substituting = p
1
x
2 p
+
5 q
=
1
4
3 p
+
6 q
=
1
3
Multiplying Throughout by 4
8 p
+
20 q
=
1
Substituting = q
1
y
Multiplying Throughout by 3
9 p
+
18 q
=
1
... (i)
... (ii)
Comparing (i) and (ii),
RHS of (i) and (ii) is equal,
Hence, LHS will also be equal,
∴
8 p
+
20 q
=
9 p
+
18 q
∴
8 p - 9p
=
18 q – 20 q
∴
- p
=
- 2 q
∴
p
=
2 q
... (iii)
Solve by Substitution Method
By Substituting (iii) in (i)
We will get p =
and q =
1
18
1
36
Re substitute p =
and q =
1
x
1
y
x
=
18
y
=
36
18 days and Man will take
36 days to complete the
work alone