Question

Two water taps together can fill a tank
$9\frac{3}{8}$
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 step can separately fill the tank.

Answer 1

hope you get the solution....

Answer 2

SOLUTION :  

Given : Two water taps together can fill a tank in 9 ⅜ = 75/8 h

Let the smaller tap fill the tank  in ‘x’ hours

The tap of larger diameter fills the tank in ‘x – 10’ hours.

In 1 hour the smaller tap fills the portion of the tank : 1/x  

In 75/8 hour the smaller tap fills the portion of the tank : 75/8 ×  1/x  = 75/8x

In 1 hour the tap of larger diameter  fills the portion of the tank : 1/(x - 10)

In 75/8 hour the tap of larger diameter fills the portion of the tank : 75/8 × 1/(x - 10) = 75/8(x - 10)

A.T.Q

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

[By taking LCM]

{x - 10 + x}/(x² - 10x) = 8/75

75(x + x – 10) = 8(x² – 10x)

75(x + x – 10) = 8x² – 80x

75(2x– 10) = 8x² – 80x

150x – 750 = 8x² – 80x

8x² – 80x - 150x + 750 = 0

8x² – 230x + 750 = 0

2(4x² – 115x + 375) = 0

4x² – 115x + 375 = 0

4x² – 100x – 15x + 375 = 0

[By middle term splitting]

4x(x – 25) – 15(x – 25) = 0

(4x – 15)(x – 25) = 0

(4x – 15) = 0 (x – 25) = 0

x = 15/4 or x = 25  

Value of x can’t be 15/4 as (x – 10) will be negative. Since, time cannot be negative,  

Therefore,  x = 25

The smaller tap fill the tank  = x = 25  hours

The tap of larger diameter fills the tank =  (x – 10) = 25 - 10 = 15 h

Hence, the time taken by the tap of larger diameter be 15 h &  time taken by smaller  tap be 25 hours.

HOPE THIS ANSWER WILL HELP YOU….