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Asked by Ashwini Last Modified
Answer 
Let the time taken by the smaller diameter tap be A hours
Let the time taken by the larger diameter tap be A-10 hours
Total time taken with both Taps together= 9 3/8 = 75 /8 hours
Amount filled in one hour by smaller diameter tap = 1/A [use concept of proportions, in A hours it fills 1 complete unit then in 1 hour it will fill 1/A units]
and by larger diamter tap = 1/(A-10) units
As it takes 75/8 hours to fill complete unit .... in 1 hour it will fill 1/(75/8) = 8/75
[1/A] + [1/(A-10)] = 8/75
Take LCM
(A-10+A)/[A*(A-10)] = 8/75
(2A-10)/(A²-10A) = 8/75
8(A²-10A) = 75 ×(2A-10){cross multiply}
8/2 (A²-10A) = 75 (A-5) {taking 2 common and dividing}
4A²-40A = 75A-375
4A² -40A-75A +375 = 0
4A²-115A + 375 = 0
4A²-100A-15A +375 = 0
4A(A-25)-15(A-25)=0
(A-25)(4A-15)
A= 25 hours
or
A= 15/4 hours
If A= 25 hours
then A-10 = 25-10 = 15 hours
if A = 15/4 hours
then A-10 = 15/4 - 10 = 15-40/4 = -25/4 hours which is not possible
since time cannot be negative therefore A = 25 hours
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Let the time taken by the smaller diameter tap = x
larger = x-10
total time taken = 75 /8
portion filled in one hour by smaller diameter tap = 1/x
and by larger diamter tap = 1/x-10
1/x + 1/x-10 = 8/75
x-10+x/x(x-10) = 8/75
2x+10/x²-10x = 8/75
8(x²-10x) = 75 ×2 (x-5)
8/2 (x²-10x) = 75 (x-5)
4x²-40x = 75x-375
4x² -40x-75x +375 = 0
4x²-115x + 375 = 0
4x²-100x-15x +375 = 0
4x(x-25)-15(x-25)=0
(x-25)(4x-15)
x= 25
x= 15/4
If x= 25
the x-10 = 25-10 = 15
if x = 15/4
x-10 = 15/4 - 10 = 15-40/4 = -25/4
since time cannot be negative therefore x = 25.
read less
Mandeep Kaur
Computer Programming Languages Trainer (Javascript , Python etc)
Let the time taken by the smaller diameter tap = x
larger = x-10
total time taken = 75 /8
portion filled in one hour by smaller diameter tap = 1/x
and by larger diamter tap = 1/x-10
1/x + 1/x-10 = 8/75
x-10+x/x(x-10) = 8/75
2x+10/x²-10x = 8/75
8(x²-10x) = 75 ×2 (x-5)
8/2 (x²-10x) = 75 (x-5)
4x²-40x = 75x-375
4x² -40x-75x +375 = 0
4x²-115x + 375 = 0
4x²-100x-15x +375 = 0
4x(x-25)-15(x-25)=0
(x-25)(4x-15)
x= 25
x= 15/4
If x= 25
the x-10 = 25-10 = 15
if x = 15/4
x-10 = 15/4 - 10 = 15-40/4 = -25/4
Since ,
Time cannot be negative
Therefore x = 25
read lessView 5 more Answers
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