Aptitude - Boats and Streams - Discussion
Discussion Forum : Boats and Streams - General Questions (Q.No. 8)
8.
A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:
Answer: Option
Explanation:
Let the speed of the stream x mph. Then,
Speed downstream = (10 + x) mph,
Speed upstream = (10 - x) mph.
 |
36 | - | 36 | = | 90 |
| (10 - x) | (10 + x) | 60 |
72x x 60 = 90 (100 - x2)
x2 + 48x - 100 = 0
(x+ 50)(x - 2) = 0
x = 2 mph.
Discussion:
85 comments Page 7 of 9.
Hussain peera said:
1 decade ago
Can we find solution to this problem in different manner it means any shortcut.
Honey said:
1 decade ago
x2+48x-100 = 0.
x2+50x+2x-100 = 0.
x(x+50)-2(x+50) = 0.
(x+50)(x-2) = 0.
x = 2.
x2+50x+2x-100 = 0.
x(x+50)-2(x+50) = 0.
(x+50)(x-2) = 0.
x = 2.
Bala said:
1 decade ago
Answer: Option A.
Explanation:
Let the speed of the stream x mph. Then,
Speed downstream = (10+x) mph,
Speed upstream = (10-x) mph.
= 36-36 = 90.
= (10 - x)(10 + x)60.
= 72x x 60 = 90(100 - x2).
x2 + 48x - 100 = 0.
(x+ 50)(x - 2) = 0.
x = 2 mph.
Explanation:
Let the speed of the stream x mph. Then,
Speed downstream = (10+x) mph,
Speed upstream = (10-x) mph.
= 36-36 = 90.
= (10 - x)(10 + x)60.
= 72x x 60 = 90(100 - x2).
x2 + 48x - 100 = 0.
(x+ 50)(x - 2) = 0.
x = 2 mph.
Sireesha said:
1 decade ago
The time difference between downstream and upstream is 90 min.
Abhinn said:
1 decade ago
Please explain what does 90 min less means?
Sowmya said:
1 decade ago
Take 36 common,
36(1/(10-x)-1/(10+x)) = 90/60.
36((10+x)-(10-x))/(100-x2) = 3/2 since in Denominator is in the form (a+b)(a-b) = a2-b2.
And 90/60 = 2/3.
36((10+x-10+x)/100-x2 = 3/2.
36(2x/100-x2) = 3/2.
72x/100-x2 = 3/2.
hence 72x*2 = 3(100-x2).
3x2+144x-300 = 0.
x2+48x-100 = 0.
(x+ 50)(x - 2) = 0.
x = 2 mph.
Hope you understand guys.
36(1/(10-x)-1/(10+x)) = 90/60.
36((10+x)-(10-x))/(100-x2) = 3/2 since in Denominator is in the form (a+b)(a-b) = a2-b2.
And 90/60 = 2/3.
36((10+x-10+x)/100-x2 = 3/2.
36(2x/100-x2) = 3/2.
72x/100-x2 = 3/2.
hence 72x*2 = 3(100-x2).
3x2+144x-300 = 0.
x2+48x-100 = 0.
(x+ 50)(x - 2) = 0.
x = 2 mph.
Hope you understand guys.
Shubh said:
1 decade ago
Sorry but I am not able to understand as to how the equation 72x x 60 = 90 (100 - x2) is reduced into x2 + 48x + 100 = 0.
Could you explain in more detail?
Could you explain in more detail?
Puneeth kumar k said:
1 decade ago
Because in question they have mentioned that 90min less.
Sandeep said:
1 decade ago
In 4th problem '+' is used why '-' hear.
36/(10 - x) "-" 36/(10 + x) = 90/60.
36/(10 - x) "-" 36/(10 + x) = 90/60.
Guru said:
1 decade ago
Two roots of eqn are 2 and -50.
We can't take -ve root so 2 is the answer.
Hence the equation (x+ 50)(x - 2) = 0 from x2+ 48x + 100 = 0.
We can't take -ve root so 2 is the answer.
Hence the equation (x+ 50)(x - 2) = 0 from x2+ 48x + 100 = 0.
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