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# two taps together can fill a tank in 75/8 hours

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## Two water taps together can fill a tank in 75/8 hrs. 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.

Two water taps together can fill a tank in 75/8 hrs. 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.

Byju's Answer Standard XII Chemistry Close Packing Two water tap... Question

Two water taps together can fill a tank in 75/8 hrs. 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.

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SIMILAR QUESTIONS

Q. 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 separately fill the tank.

Q. 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 hrs.) in which tap of smaller diameter can separately fill the tank.

Q.

Two water taps together can fill a tank in 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.

Q. Two water taps together can fill a tank in

938hours

. 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.

Q. Question 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.

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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

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.

1116 129

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## Ex 4.3, 9

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

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## Ex 4.3, 9 - Chapter 4 Class 10 Quadratic Equations (Term 2)

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### Transcript

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/𝑥 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 – 10 = x – 10 hours Volume of Tank filled by larger tap in 1 hour = 1/(𝑥 −10) 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/𝑥 Tank filled by smaller tap in 75/8 hrs. = 1/𝑥×75/8 = 75/8𝑥 Also, Tank filled by larger tap in 1 hrs. = 1/(𝑥 − 10) Tank filled by larger tap in 75/8 hours = 1/(𝑥 −10)×75/8=75/(8(𝑥−10)) Tank filled by smaller tap + tank filled by larger tap = 1 75/8𝑥+75/(8(𝑥 − 10))=1 75/8 (1/𝑥+1/(𝑥 − 10))=1 1/𝑥+1/(𝑥 − 10)=8/75 (𝑥 −10 + 𝑥)/(𝑥(𝑥 − 10))=8/75 (2𝑥 −10)/(𝑥2 −10𝑥)=8/75 (2x – 10) 75 = 8 (x2 – 10x) 150x – 750 = 8x2 – 80x 150x – 750 – 8x2 + 80x = 0 – 8x2 + 150x + 80x – 750 = 0 – 8x2 + 230x – 750 = 0 0 = 8x2 – 230x + 750 8x2 – 230x + 750 = 0 We solve this by quadratic method Comparing equation with ax2 + bx + c = 0, Here a = 8, b = –230, c = 750 We know that D = b2 – 4ac D = (–230)2 – 4 × 8 × ( 750) D = 52900 – 24000 D = 28900 So, the roots to equation are x = (−𝑏 ± √𝐷)/2𝑎 Putting values x = (−(−230) ± √28900)/(2 × 8) x = (230 ± √28900)/16 x = (230 ± √(289 × 100))/16 x = (230 ± √289 × √100)/16 x = (230 ± √(〖17〗^2 ) × √(〖10〗^2 ))/16 x = (230 ± 17 × 10)/16 x = (230 ± 170)/16 Solving

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