Question

12. Three taps take 6 hours, 8 hours and 10 hours
respectively to fill a tank. All three taps were
allowed to run for 2 hours and then first and second
taps were closed. How long will it take the third
tap to fill the remaining tank?
​

Answer 1

Answer:

The remaining tank will be filled by the 3rd tap in $\sf{2\dfrac{1}{2}\:hours.}$

Given:

• Time taken by 1st tap to fill the tank = 6 hours
• Time taken by 2nd tap to fill the tank = 8 hours
• Time taken by 3rd tap to fill the tank = 10 hours
• All three taps were allowed to run for 2 hours and then first and second taps were closed.

To Find:

• How long will it take the 3rd tap to fill the remaining tank?

Solution:

Time taken by 1st tap to fill the tank = 6 hours

Time taken by 2nd tap to fill the tank = 8 hours

Time taken by 3rd tap to fill the tank = 10 hours

-----------------------

Work done by 1st tap in 1 hour = 1/6

Work done by 2nd tap in 1 hour = 1/8

Work done by 3rd tap in 1 hour = 1/10

-----------------------

(1st + 2nd + 3rd) tap's 1 hour work = 1/6 + 1/8 + 1/10

$\sf{=\dfrac{20+15+10}{120}=\dfrac{45}{120}=\dfrac{3}{8}}$

$\sf{(1st + 2nd + 3rd)\: tap's\: 2 \:hour\: work = 2\times\dfrac{3}{8} =\dfrac{3}{4}}$

$\sf{Remaining\: work =\bigg(1-\dfrac{3}{4}\bigg)=\dfrac{4-3}{4}=\dfrac{1}{4}}$

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Now, 1/10 work is done by 3rd tap in one hour.

$\sf{\dfrac{1}{4}\:work\:will\:be\:done \:by \:3rd\:tap\:in\bigg(\dfrac{1}{4}\div\dfrac{1}{10}\bigg)\:hours}$

$\sf{=\dfrac{1}{4}\times10=\dfrac{5}{2}=2\dfrac{1}{2}\:hours}$

Hence, the remaining tank will be filled by the 3rd tap in $\sf{2\dfrac{1}{2}\:hours.}$

Answer 2

Step-by-step explanation:

Time taken by 1st tap to fill the tank = 6 hours

Time taken by 2nd tap to fill the tank = 8 hours

Time taken by 3rd tap to fill the tank = 10 hours

-----------------------

Work done by 1st tap in 1 hour = 1/6

Work done by 2nd tap in 1 hour = 1/8

W

ork done by 3rd tap in 1 hour = 1/10

-----------------------

working together-- 1/6+1/8+1/10

(20+12+15/120=47/120

working together work done- 47/120×2--47/60

remaining work-- 60-70/60--13/60

time taken by 3rd tap to complete remaining work.

1/10÷13/60

6/13 hours

reciprocal of 6/13-- 13/6--

2whole1/6

thus third tap will take 2hrs 10mins