Question

a water tap a takes 7 minutes more than the tap b for filling up a tank with water the tab a page 16 minutes more than the time taken by both the taps together to fill the tank find the time each each tap alone tank to fill the tank​

Answer 1

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.

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