Question

Class 10...Maths..
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Explaination Required. ​

Answer 1

Question:

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

Answer:

Smaller tap takes 25 hours

Larger tap takes 15 hours to fill the tank separately

Step-by-step explanation:

Let the time taken by Smaller tap to fill the tanks be ' x ' hours

Work done by smaller tap in 1 hour = 1/x

Time taken larger tap to fill the tank = 10 hours less than smaller tap = ( x - 10 ) hours

Work done by larger tap in 1 hour = 1 / ( x - 10 )

Time taken by both taps to fill the tank = 9 3/8 hours = 75 / 8 hours

Work done by both taps in 1 hour = 8 / 75

$\Rightarrow \sf \dfrac{1}{x} + \dfrac{1}{x - 10} = \dfrac{8}{75}$

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

⇒ 75 ( 2x - 10 ) = 8( x² - 10x )

⇒ 75( x - 5 ) = 4( x² - 10x )

⇒ 75x - 375 = 4x² - 40x

⇒ 0 = 4x² - 75x - 40x + 375

⇒ 0 = 4x² - 115x + 375

⇒ 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

If x = 15/4, ( x - 10 ) would be negative so x = 15/4 is neglected

⇒ x = 25

Time taken by smaller tap = x = 25 hours

Time taken by larger tap = ( x - 10 ) = ( 25 - 10 ) = 15 hours

Therefore the smaller tap takes 25 hours whereas larger tap takes 15 hours separatetely to fill the tank.

Answer 2

Answer:

above answer is correct mark it as brainlies