12. Three taps take 6 hours, 8 hours and 10 hoursrespectively to fill a tank. All three taps wereallowed to run for 2 hours and then first and secondtaps were closed. How long will it take the thirdtap to fill the remaining tank? About the author Mia
Answer: The remaining tank will be filled by the 3rd tap in [tex]\sf{2\dfrac{1}{2}\:hours.}[/tex] 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 [tex]\sf{=\dfrac{20+15+10}{120}=\dfrac{45}{120}=\dfrac{3}{8}}[/tex] [tex]\sf{(1st + 2nd + 3rd)\: tap’s\: 2 \:hour\: work = 2\times\dfrac{3}{8} =\dfrac{3}{4}}[/tex] [tex]\sf{Remaining\: work =\bigg(1-\dfrac{3}{4}\bigg)=\dfrac{4-3}{4}=\dfrac{1}{4}}[/tex] ———————– Now, 1/10 work is done by 3rd tap in one hour. [tex]\sf{\dfrac{1}{4}\:work\:will\:be\:done \:by \:3rd\:tap\:in\bigg(\dfrac{1}{4}\div\dfrac{1}{10}\bigg)\:hours}[/tex] [tex]\sf{=\dfrac{1}{4}\times10=\dfrac{5}{2}=2\dfrac{1}{2}\:hours}[/tex] Hence, the remaining tank will be filled by the 3rd tap in [tex]\sf{2\dfrac{1}{2}\:hours.}[/tex] Reply
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 Reply
Answer:
The remaining tank will be filled by the 3rd tap in [tex]\sf{2\dfrac{1}{2}\:hours.}[/tex]
Given:
To Find:
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
[tex]\sf{=\dfrac{20+15+10}{120}=\dfrac{45}{120}=\dfrac{3}{8}}[/tex]
[tex]\sf{(1st + 2nd + 3rd)\: tap’s\: 2 \:hour\: work = 2\times\dfrac{3}{8} =\dfrac{3}{4}}[/tex]
[tex]\sf{Remaining\: work =\bigg(1-\dfrac{3}{4}\bigg)=\dfrac{4-3}{4}=\dfrac{1}{4}}[/tex]
———————–
Now, 1/10 work is done by 3rd tap in one hour.
[tex]\sf{\dfrac{1}{4}\:work\:will\:be\:done \:by \:3rd\:tap\:in\bigg(\dfrac{1}{4}\div\dfrac{1}{10}\bigg)\:hours}[/tex]
[tex]\sf{=\dfrac{1}{4}\times10=\dfrac{5}{2}=2\dfrac{1}{2}\:hours}[/tex]
Hence, the remaining tank will be filled by the 3rd tap in [tex]\sf{2\dfrac{1}{2}\:hours.}[/tex]
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