Question

please solve please please please please please please.
By quadratic equation class 10 th. ​

Answer 1

Let the time taken to fill the tank by larger tap be x hrs

Let the time taken to fill the tank by smaller tap be

(x +10) hrs

Larger tap can fill the tank in hour = 1/x

Smaller tap can fill the tank in hour = 1/x+10

ATQ

$( \frac{1}{x + 10} ) \frac{75}{8} +( \frac{1}{x} ) \frac{75}{8} = 1 \\ \\ \frac{7}{8x + 80} + \frac{75}{8x} = 1 \\ \\ \frac{75 + 75(x + 10)}{8x(x + 10)}$

75x +75x + 750 = 8x² +80x

150x - 80x +750 - 8x² =0

8x²-70x - 750 = 0

By quadratic formula method

D = b² - 4ac

= (-70)² - 4(8)(-750)

= 4900 + 24000 = 28900

x = - b±√D /2a

= 70 +√28900/26

= 70 + 170/16.

= 15

Or, x = 70 - √28900/26

x = 70 - 170/16

x = -100/6

It is rejected as time can't be negative

_______________________

Larger tap fill the tank in 15 hours

Smaller tap to fill the tank = 15 +10 = 25 hours.

.

Hope it helps

Thanks for asking

☘ℙ☘

Answer 2

Let the time taken by the smaller diameter tap = x hours

Then time taken by larger tap = (x-10) hours

Time taken by both taps to fill the tank = 75 /8

Portion filled in 1 hour by smaller tap = 1/x

Portion filled in 1 hour by larger tap = 1/(x-10)

Portion filled by both taps in 1 hour = 8/75

Now,

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

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

2x-10 / x²-10x = 8/75

2( x-5) / x²-10x = 8/75

8 (x²-10x) = 75 ×2 (x-5) {cross multiplying}

8/2 (x²-10x) = 75 (x-5)

4x²-40x = 75x-375

4x² -40x-75x +375 = 0

4x²-115x + 375 = 0 ------ (1)

By splitting the middle term

4x²-115x +375=0

4x²-100x-15x +375 = 0

4x(x-25)-15(x-25)=0

(x-25)( 4x-15)

x= 25

x= 25x= 15/4

By quadratic formula method

From eq (1)

a= 4 , b= -115 , c= 375

D = b² - 4ac

= (-115)² - 4(4)(375)

= 13225 - 6000 = 7225

x = - b± √D /2a

=[ -(-115) ±√7225 ] /8

= [115 +85] /8 , [115-85] /8

= 200 / 8 , 30 / 8

=> x= 25 , x= 15 /4

taking x= 25 

then time taken by larger tap

=> x-10 = 25-10 = 15

taking x = 15/4

then time taken by larger tap

=> x-10 = 15/4 - 10 = 15-40/4 = -25/4

since time cannot be negative therefore x = 25