# 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 a smaller diameter fill the tank in x hours.

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

In x hours, a smaller tap fills the tank.

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

In (x -10) hours, a larger tap fills the tank.

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

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

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

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

By taking LCM and cross multiplying:

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

2x - 10/(x^{2} - 10x) = 8/75

75(2x - 10) = 8(x^{2} - 10x)

150x - 750 = 8x^{2} - 80x

8x^{2} - 80x - 150x + 750 = 0

8x^{2} - 230x + 750 = 0

4x^{2} - 115x + 375 = 0

We will solve this quadratic equation using the quadratic formula.

Comparing with ax^{2} + 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 ± √(b^{2} - 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.

Time taken by smaller tap x = 25 hours

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

**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:

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

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