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

    Two water taps together can fill a tank in 9 (3/8) hours.The tap of larger diameter takes 10 hrs less than the smaller one to fill the tank separately.Find the time in which each tap can separately fill the tank. - Get the answer to this question by visiting BYJU'S Q&A Forum.

    Academic QuestionsMaths QuestionsTwo Water Taps Together Can Fill A Tank In 9 3 8 Hours The Tap Of Larger Diameter Takes 10 Hrs Less Than Smaller One To Fill The Tank Separately Find The Time In Which Each Tap Can Separately Fill

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

    Answer:

    Let the tap with smaller diameter fills the tank alone in x hours

    Let the tap with larger diameter fills the tank alone in (x – 10) hours.

    In 1 hour, the tap with a smaller diameter can fill 1/x part of the tank.

    In 1 hour, the tap with larger diameter can fill 1/(x – 10) part of the tank.

    The tank is filled up in 75/8 hours.

    Thus, in 1 hour the taps fill 8/75 part of the tank.

    1/x + 1/(x-10) = 8/75

    (x-10) + x / x(x-10) = 8/75

    2x – 10/x(x-10) = 8/75

    75 (2x-10) = 8(x2-10x) by cross multiplication

    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, and the time taken by the larger tap to fill the tank = ( 25 – 10 ) = 15 hours.

    For further reference, check out the video

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    Two water taps together can fill a tank in 9 38 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time(in hrs.) in which tap of smaller diameter can separately fill the tank.

    Click here👆to get an answer to your question ✍️ Two water taps together can fill a tank in 9 38 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time(in hrs.) in which tap of smaller diameter can separately fill the tank.

    Two water taps together can fill a tank in 9

    Question 8 3 ​

    hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time(in hrs.) in which tap of smaller diameter can separately fill the tank.

    A

    25

    B

    4 −25 ​

    C

    24

    D

    4 25 ​ Medium Open in App Solution Verified by Toppr

    Correct option is A)

    Consider that the tap with smaller diameter fills the tank in x hours.

    Then, the tap with larger diameter fills the tank in x−10 hours.

    This shows that the tap with a smaller diameter can fill

    x 1 ​

    part of the tank in 1 hour. Similarly, the tap with larger diameter can fill

    x−10 1 ​

    part of the tank in 1 hour.

    It is given that the tank is filled in

    8 75 ​

    hours that is, the taps fill

    75 8 ​

    part of the tank in 1 hour. Then,

    x 1 ​ + x−10 1 ​ = 75 8 ​ x(x−10) x−10+x ​ = 75 8 ​ x 2 −10x 2x−10 ​ = 75 8 ​ 75(2x−10)=8(x 2 −10x) 150x−750=8x 2 −80x 8x 2 −230x+750=0 4x 2 −115x+375=0 4x 2 −100x−15x+375=0 4x(x−25)−15(x−25)=0 (4x−15)(x−25)=0 4x−15=0 x= 4 15 ​ Or, x−25=0 x=25 When x= 4 15 ​ , then, x−10= 4 15 ​ −10 = 4 15−40 ​ =− 4 25 ​

    This cannot be possible because time can never be negative.

    When x=25, then, x−10=25−10 x=25

    Therefore, the tap of smaller diameter can separately fill the tank in 25 hours.

    Was this answer helpful?

    599 61

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    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.

    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? Then the time taken by smaller tap is 25 hours and the time taken by the larger tap is 15 hours.

    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.

    Solution:

    Let the tap of smaller diameter fill the tank in x hours.

    The tap of larger diameter takes (x - 10) hours.

    Given, the two water taps can fill the tank together in 9 3/8 hours = 75/8 hours

    The smaller tap fills the tank in x hours.

    Therefore, in one hour, the part of the tank filled by the smaller tap = 1/x

    Also, the larger tap fills the tank in (x - 10) hours.

    Thus, in one hour, the part of the tank filled by the larger tap = 1/(x - 10)

    Now, considering both the pipes working together we have,

    In 1 hour, the part of the tank filled by the smaller and larger tap together is,

    1/x + 1/(x - 10) = 8/75 [ Since, the two water taps can fill the tank together in 75/8 hours]

    By taking LCM and solving,

    (x - 10 + x) / x(x -10) = 8/75

    (2x - 10) / (x2 - 10x) = 8/75

    75(2x - 10) = 8(x2 - 10x)

    150x - 750 = 8x2 - 80x

    8x2 - 80x - 150x + 750 = 0

    8x2 - 230x + 750 = 0

    4x2 - 115x + 375 = 0

    We will solve this quadratic equation using the quadratic formula.

    Comparing 4x2 - 115x + 375 = 0 with ax2 + bx + c = 0, we get a = 4, b = - 115, c = 375

    b² - 4ac = (- 115)2 - 4(4)(375)

    = 13225 - 6000 = 7225 b² - 4ac > 0

    Hence, real roots exist.

    x = [- b ± √(b2 - 4ac)] / 2a

    x = (115 ± √7225) / 8

    x = (115 + 85) / 8 and x = (115 - 85) / 8

    x = 200/8 and x = 30/8

    x = 25 and x = 15/4

    x cannot be 15/4 hours because the larger tap takes 10 hours less than x and this would give us a negative value as 15/4 <10.

    Thus, x = 25

    Time taken by smaller tap x = 25 hours

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

    ☛ Check: NCERT Solutions for Class 10 Maths Chapter 4Video Solution:

    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

    Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.3 Question 9

    Summary:

    If two water taps together can fill a tank in 9 3/8 hours and the tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately, then the time taken by the smaller tap is 25 hours and the time taken by the larger tap is 15 hours to separately fill the tank.

    ☛ Related Questions:

    Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.

    Find the roots of the following equations:(i) x - 1/x = 3, x ≠ 0(ii) 1/(x + 4) - 1/(x - 7) = 11/30, x ≠ - 4, 7

    The sum of the reciprocals of Rehman’s age (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

    In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had She got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

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