QUADRATIC �EQUATIONS
+ x
x + 10
x(x + 10)
=
1
12
2x + 10
x2 + 10x
=
1
12
Work done by John in 1 day =
Work done by Ganesh in 1 day =
Work done by both in 1 day =
As per the given condition,
+
=
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Q)
Sol.
Let the number of days required by John alone to complete the work be x days.
No. of days taken by Ganesh alone is (x + 10) days.
Also number of days required by both to
complete the same work is 12 days
Work
No. of days
Work done in 1 day
1
2
1/2
3
1/3
6
1/6
12
x
x+10
1/x+10
1
1
1
1
1
To do one work
Work done in one day
It takes two days
1 (x2 + 10x)
24x
x2
x2
x2
x
(x – 20)
x – 20 = 0
x = 20
The numbers of days cannot be negative
Hence, x = 20
x + 10
Ganesh alone worked for 30 days.
1
Find two factors of 120 in such a way that by subtracting factors we get middle no. 14
Since we are subtracting the factors give middle term sign to the bigger factor and the opposite sign to the smaller factor
2
6
12
–
+
– 20x
+ 6x
– 120
= 0
(x – 20)
+ 6
(x – 20)
= 0
(x + 6)
= 0
or x + 6 = 0
or x = – 6
= 20 + 10
= 30
– 14x
– 120
= 0
What we need to find ?
It is given that …
x ≠ – 6
= 12 (2x + 10)
+ 120
x2
+ 10x =
= 0
+ 10x
– 24x
– 120
1/12
1/x
In a comparative statement whatever comes later is taken as x
0
0
For doing some work Ganesh takes 10 days more than John. If both work together they complete the work in 12 days. Find the number of days if Ganesh worked alone?
6
–
= 14
20