NTSE Stage 2 MAT 2015 Question Paper

Let first, second and third pipe be A, B & C.
According to question,
B=A−5 ...(i)
B=c+4 ...(ii)
Let the time required by the first pipe to fill the tank be x hr
From equation (i)
B=x−5
From equation (ii)
c=x−9
Again According to question

1

A

+

1

B

=

1

C

1

x

+

1

x−5

=

1

x

−9
(2x−5)(x−9)=x(x−5)
x2−18x+45=0
x2−15x−3x+45=0
x(x−15)−3(x−15)=0
x=3=0
∴ x=3 is not possible
∴ x−15=0 ∴ x=15
So, the time required by the first pipe to fill the tank is 15 hours.