Last updated at Feb. 25, 2017 by Teachoo

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Ex 4.3 ,9 Two water taps together can fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank. Let the time taken by smaller tap to fill tank completely = x hours So, Volume of tank filled by smaller tap in 1 hour = 1/๐ฅ Also , it is given that time take by larger tap is 10 hour less Time taken by larger tap to fill tank completely = Time taken by smaller tap โ 10 = x โ 10 hours Volume of Tank filled by larger tap in 1 hour = 1/(๐ฅ โ10) Now, it is given that Time taken by both taps to fill = 9 3/8 hours = (9(8)+ 3)/8 hours = 75/8 hours Also, Tank filled by smaller tap in 1 hrs. = 1/๐ฅ Tank filled by smaller tap in 75/8 hrs. = 1/๐ฅร75/8 = 75/8๐ฅ Also, Tank filled by larger tap in 1 hrs. = 1/(๐ฅ โ 10) Tank filled by larger tap in 75/8 hours = 1/(๐ฅ โ10)ร75/8=75/(8(๐ฅโ10)) Tank filled by smaller tap + tank filled by larger tap = 1 75/8๐ฅ+75/(8(๐ฅ โ 10))=1 75/8 (1/๐ฅ+1/(๐ฅ โ 10))=1 1/๐ฅ+1/(๐ฅ โ 10)=8/75 (๐ฅ โ10 + ๐ฅ)/(๐ฅ(๐ฅ โ 10))=8/75 (2๐ฅ โ10)/(๐ฅ2 โ10๐ฅ)=8/75 (2x โ 10) 75 = 8 (x2 โ 10x) 150x โ 750 = 8x2 โ 80x 150x โ 750 โ 8x2 + 80x = 0 โ 8x2 + 150x + 80x โ 750 = 0 โ 8x2 + 230x โ 750 = 0 0 = 8x2 โ 230x + 750 8x2 โ 230x + 750 = 0 We solve this by quadratic method Comparing equation with ax2 + bx + c = 0, Here a = 8, b = โ230, c = 750 We know that D = b2 โ 4ac D = (โ230)2 โ 4 ร 8 ร ( 750) D = 52900 โ 24000 D = 28900 So, the roots to equation are x = (โ๐ ยฑ โ๐ท)/2๐ Putting values x = (โ(โ230) ยฑ โ28900)/(2 ร 8) x = (230 ยฑ โ28900)/16 x = (230 ยฑ โ(289 ร 100))/16 x = (230 ยฑ โ289 ร โ100)/16 x = (230 ยฑ โ(ใ17ใ^2 ) ร โ(ใ10ใ^2 ))/16 x = (230 ยฑ 17 ร 10)/16 x = (230 ยฑ 170)/16 Solving

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.