) A water tap A takes 7 minutes more than water tap B for filling up a

1.	) A water tap A takes 7 minutes more than water tap B for filling up a tank with waterThe tap A takes 16 minutes more than the time taken by both the taps together to fillthe tank. Find the time each tap alone would take to fill the tank.
Answer» Let the time taken by A is x minutes and B is y minutes, Hence from the 1st statement we have, x-y = 7 = > y = x-7..........................eq1 Now, in one minute tank filled by A = 1/x and in one minute tank filled by B = 1/y So combine together both can fill = 1/x + 1/y tank in one minute, Hence time taken by both the taps to fill the tank = 1/(1/x + 1/y) = xy/x+y Now from the second statement, x- xy/x+y = 16 => x² + xy - xy = 16(x+y) => x² -16x - 16y = 0 Putting the value of y from eq1 x²-16x - 16(x-7) = 0 => x² - 32x + 112 = 0. Solving the above quadratic eqn, we get x = 28 or 4 rejecting 4 as x can't be less than 7 x = 28 y = x-7 = 28-7 = 21 Hence time taken by both the taps are 28 and 21 minutes alone.

) A water tap A takes 7 minutes more than water tap B for filling up a tank with waterThe tap A takes 16 minutes more than the time taken by both the taps together to fillthe tank. Find the time each tap alone would take to fill the tank.

Answer»

Let the time taken by A is x minutes and B is y minutes,

Hence from the 1st statement we have,

x-y = 7 = > y = x-7..........................eq1

Now, in one minute tank filled by A = 1/x

and in one minute tank filled by B = 1/y

So combine together both can fill = 1/x + 1/y tank in one minute,

Hence time taken by both the taps to fill the tank

= 1/(1/x + 1/y)

= xy/x+y

Now from the second statement,

x- xy/x+y = 16

=> x² + xy - xy = 16(x+y)

=> x² -16x - 16y = 0

Putting the value of y from eq1

x²-16x - 16(x-7) = 0

=> x² - 32x + 112 = 0.

Solving the above quadratic eqn, we get

x = 28 or 4

rejecting 4 as x can't be less than 7

x = 28

y = x-7 = 28-7 = 21

Hence time taken by both the taps are 28 and 21 minutes alone.