QUADRATIC EQUATIONS
Portion of the tank filled in 1 hour by both taps
∴ The time taken by a larger tap
= (x – 10) hours
Sol :
Let the time taken to fill a tank by smaller tap be ‘x’ hrs.
Time taken by both the taps together to fill the same tank
As per the given condition,
∴
∴
150x
= 8x2
∴
–8x2
∴
–8x2
Dividing throughout by – 2
∴
4x2
- 115x
+ 375
= 0
∴
4x2
– 100x – 15x
+ 375
= 0
∴
4x
– 15
= 0
∴
(x -25)
(4x – 15)
= 0
∴
x -25 = 0
or
4x – 15 = 0
∴
x = 25
or
4x = 15
∴
x = 25
or
Hence x = 25
∴ x - 10
= 25 – 10
= 15
What we have to find in this sum ?
Since last sign is ‘+’ Give middle sign to the both the factors
100
15
1500
–
–
375 × 4 = 1500
∴
∴
∴
In a comparative statement whatever comes later is taken as ‘x’
+ 80x
+ 150x
– 750
= 0
+ 230x
– 750
= 0
‘+’ sign means adding
Find two factors of 1500 in such a way that by adding factors we get middle number.
(x – 25)
(x – 25)
Time taken by larger tap alone is 15 hours and by smaller tap alone is 25 hours
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1
Time required to fill a tank
Portion of tank filled in 1hour
1
3 hrs
1
2 hrs
Tank
1
x hrs
x – 10 hrs
1
Smaller tap
Larger tap
Both taps
EX 4.3 9