Question

Two pipes together can fell a tank in 12 mich. Pipe A
alone takes 32 minute more than pipe B alone to
fill the tank. find in how much time «pipe A
alone fill the tank.​

Answer 1

Answer:

Pipe A alone will take 48 minutes to fill the tank

Step-by-step explanation:

No. of minutes taken by pipe B to fill the tank = x

=> No. of minutes taken by pipe A to fill the tank = x + 32

Hence,

Fraction of tank filled by pipe B in 1 minute = 1/x

Fraction of tank filled by pipe A in 1 minute = 1/(x + 32)

Hence,

Fraction of tank filled by pipe B in 12 minutes = 12/x

Fraction of tank filled by pipe A in 12 minutes = 12/(x + 32)

=> The fraction of tank filled by pipe A and B together in 12 minutes

= 12/x + 12/(x + 32) ............(i)

We are given that pipes A and B together fill the tank completely in 12 minutes

=> Fraction of tank filled by both pipes A and B together in 12 minutes = 1

=> $\frac{12}{x} + \frac{12}{x+32} = 1$

=> 12(x + 32) + 12x = x(x + 32)

=> 12x + 384 + 12x = x² + 32x

=> 24x + 384 = x² + 32x

=> x² + 32x - 24x - 384 = 0

=> x² + 8x - 384 = 0

=> x² + 24x - 16x - 384 = 0

=> (x + 24)(x - 16) = 0

=> x = 16

[As x stands for number of minutes, negative values are inadmissible.]

Hence:

No. of minutes taken by Pipe B to fill the tank = x = 16

No. of minutes taken by Pipe A to fill the tank = x+32 = 48

Answer: Pipe A will take 48 minutes to fill the tank.

Verification:

Fraction of tank filled by pipe A in 12 minutes = 12*(1/48) = 1/4

Fraction of tank filled by pipe B in 12 minutes = 12*(1/16) = 3/4

In 12 minutes, pipe A and B will fill (1/4 + 3/4) of the tank.

This means pipe A and B will fill the tank completely in 12 minutes √

Hence, verified.