Question

In the kitchen there are two pipes a and
b. Pipe b take 5 more minutes than pipe a to fill a vessel. While the two pipes a and b when opened together can fill the vessel in 6 minutes, then find time in which a and b can fill the tank separately will be respectively?

Answer 1

Answer:

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Pipe A can fill a vessel in A mins

then pipe can fill in 1 min = 1/A

Pipe B take 5 more minutes than Pipe A to fill a vessel

Pipe B can fill in A + 5 Mins

Pipe A & B can fill vessel together in 6 Mins

Pipe A & B can fill vessel  in 1 min = 1/6

=> 1/A  + 1/(A + 5) = 1/6

=> 6(A + 5) + 6A = A(A + 5)

=> 6A + 30 + 6A = A² + 5A

=> A² - 7A - 30 = 0

=>A² - 10A + 3A - 30 = 0

=> A(A - 10) + 3(A - 10) = 0

=> (A + 3)(A - 10) =0

=> A = 10

Pipe A can fill in 10 mins

Pipe B can fill in 10 + 5 = 15 mins

A and B can fill the tank separately in 10 & 15 mins respectively

Answer 2

[HeY Mate]

Answer:

Pipe A can fill a vessel in x mins

then pipe can fill in 1 min = 1/x

Pipe B take 5 more minutes than Pipe A to fill a vessel

Pipe B can fill in x + 5 Mins

Pipe A & B can fill vessel together in 6 Mins

Pipe A & B can fill vessel in 1 min = 1/6

=> 1/x + 1/(x + 5) = 1/6

=> 6(x + 5) + 6x = x(x + 5)

=> 6x + 30 + 6x = x² + 5x

=> x² - 7x - 30 = 0

=>x² - 10x + 3x - 30 = 0

=> x(x - 10) + 3(x - 10) = 0

=> (x + 3)(x - 10) =0

=> x = 10

Pipe A can fill in 10 mins

Pipe B can fill in 10 + 5 = 15 min.

A and B can fill the tank separately in 10 and 15 min.

I Hope It Helps You✌️