# two water taps together can fill a tank in 3 9 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 9Question 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.

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## Two water taps together can fill a tank in 93/8 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 93/8 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.

Byju's Answer Standard X Mathematics Quadratic Formula Two water tap... Question

Two water taps together can fill a tank in

938 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.

Open in App Solution

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

1x part of the tank. In 1

hour, the tap with larger diameter can fill

1x-10 part of the tank.

The tank is filled up in

=938=758 hrs Thus, in 1 hour the taps fill 875 part of the tank.

Now, according to question,

1x+1x-10=758 x-10+xxx-10=875 752x-10=8xx-10 150x-750=8x2-80x 8x2-80x-150x+750=0 8x2-230x+750=0 4x2-115x+375=0 4x2-100x-15x+375=0 4xx-25-15x-25=0 4x-15x-25=0 4x-15=0 x-25=0 x=154 x=25

Now, there are two values of

x .

Therefore, we will have two cases.

**Case (a)- When**

x=154 hrs , then

x-10=154-10=-254 hrs

.

Since, time cannot be in negative. therefore this case is not possible.

**Case (b)- When**

x=25 hrs x-10=25-10=15 hrs .

**∴ Hence, 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**

15 hours. Suggest Corrections 6

SIMILAR QUESTIONS

**Q.**

Two water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 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.

**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.

**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.

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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 4

**Video 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:**

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