Question

Two water taps together can fill a tank 9 and 3/8 hours. The tap of larger diameter takes 10 hour less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank ?

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Answer 1

Let us consider the time taken by the smaller diameter tap = x

The time is taken by the larger diameter tap = x – 10

Totaltimeistakentofillatank=938

Total time is taken to fill a tank = 75/8

In one hour portion filled by smaller diameter tap = 1/x

In one hour portion filled by larger diameter tap = 1/(x – 10)

In one hour portion filled by taps = 8/75

⇒ 1x+1x−10=875 x−10+xx(x−10)=875 2x−10x2−10x=875

75 (2x-10) = 8(x2-10x)

150x – 750 = 8x2 – 80x

8x2 − 230x + 750 = 0

4x2−115x + 375 = 0

4x2 − 100x −15x + 375 = 0

4x(x−25)−15(x−25) = 0

(4x−15)(x−25) = 0

4x−15 = 0 or x – 25 = 0

x = 15/4 or x = 25

Case 1: When x = 15/4

Then x – 10 = 15/4 – 10

⇒ 15-40/4

⇒ -25/4

Time can never be negative so x = 15/4 is not possible.

Case 2: When x = 25 then

x – 10 = 25 – 10 = 15

∴ The tap of smaller diameter can separately fill the tank in 25 hours

....follow mw....

Answer 2

Let the smaller tank fill the tank in x hours

then the larger fills the tank in (x-10) hours

Time taken by both taps together to fill the tank =$\sf{9 \frac{3}{8} h = \frac{75}{8} h}$

Part of tank filled by the smaller tap in 1h = $\sf{\frac{1}{x}}$

Part of tank filled by the larger tap in 1h = $\sf{\frac{1}{x-10}}$

Part of tank filled by both taps together in 1h = $\sf{\frac{8}{75}}$

$\therefore$ $\sf{\frac{1}{x} + \frac{1}{x + 10} = \frac{8}{75}}$

$\sf{ \frac{(x + 10) + x}{x(x - 10)} = \frac{8}{75}}$

$\sf{\frac{2x - 10}{ {x}^{2} - 10x } = \frac{8}{75}}$

$\sf{ {8x}^{2} - 80x = 150x - 750}$

$\sf{ {8x}^{2} - 230x + 750 = 0}$

$\sf{ {4x}^{2} - 115x + 375 = 0}$

$\sf{{4x}^{2} - 100x - 15x + 375 = 0}$

$\sf{4x(x - 25) - 15(x - 25) = 0}$

$\sf{(x - 25)(4x - 15) = 0}$

$\sf{x = 25 = 0 \: or \: 4x - 15 = 0}$

$\sf{x = 25 \: or \: x = \frac{15}{4}}$

$\sf{x = \frac{15}{4}}$

$\sf{x - 10 < 0}$

i.e, the time taken by the larger pipe is negative which is not possible, So x= 25.

Hence, the time taken by the smaller tap to fill the tank = 25h

And time taken by the larger tap to fill the tank = 25 - 10 = 15h