Question

★ 100 Points Question ★
For Maths genius .

Two water taps together can fill a tank in ( 9 whole 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 tab can separately fill the tank.

Quality answer required .

Answer 1

$\huge \bf \pink{ \mathcal{H}ey \: there !! }$


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

→ Then, the larger tap fills it in ( x - 10 ) hours .

→ Time taken by both together to fill the tank = $\frac{75}{8}$ hours .

→ Part filled by the smaller tap in 1 hr = $\frac{1}{x}$ .

→ Part filled by the larger tap in 1 hr = $\frac{1}{ ( x - 10 ) }$ .

→ Part filled by both the taps in 1 hr = $\frac{8}{75}$ .


$\sf \therefore \frac{1}{x} + \frac{1}{(x - 10)} = \frac{8}{75} . \\ \\ \sf \implies \frac{(x - 10) + x}{x(x - 10)} = \frac{8}{75} . \\ \\ \sf \implies \frac{(2x - 10)}{x(x - 10)} = \frac{8}{75} . \\ \\ \sf \implies75(2x - 10) = 8x(x - 10). \: \: \: (by \: cross \: multiplication) \\ \\ \sf \implies150x - 750 = 8 {x}^{2} - 80x. \\ \\ \sf \implies8 {x}^{2} - 230x + 750 = 0. \\ \\ \sf \implies4 {x}^{2} - 115x + 375 = 0. \\ \\ \sf \implies4 {x}^{2} - 100x - 15x + 375 = 0. \\ \\ \sf \implies4x(x - 25) - 15(x - 25) = 0. \\ \\ \sf \implies(x - 25)(4x - 15) = 0. \\ \\ \sf \implies x - 25 = 0. \: \: or \: \: 4x - 15 = 0. \\ \\ \sf \implies x = 25 \: \: or \: \: x = \frac{15}{4} . \\ \\ \sf \implies x = 25 \: \: ( \therefore x = \frac{15}{4} \implies(x - 10) < 0).$



✔✔ Hence, the time taken by the smaller tap to fill the tank = $\huge \boxed{ \green{ 25 hours }}$ .

And, the time taken by the larger tap to fill the tank = ( 25 - 10 ) hrs = $\huge \boxed{ \green{ 15 hours }}$ . ✅✅



$\huge \boxed{ \blue{ \mathbb{THANKS}}}$

Answer 2

Two water taps together can fill a tank in ( 9 whole 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 tab can separately fill the tank.

Let time taken by pipe of larger diameter P1 be x.

Then time by smaller one P2 = (x+10).

work of P1 of 1hr = 1/x,

work of P2 of 1hr = 1/(x+10)

Both are working together,

1hr work = 1/x + 1/(x+10)

Work in 75/8 hrs = 1

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

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

=) 75(2x+10) = 8(x²+10x)

=) 150x + 750 = 8x² + 80x

=) 8x² - 70x - 750 = 0

=) 4x² - 35x - 375 = 0

By factorization,

x = 15,

P1's time = 15hrs,

P2 = (15+10) = 25hrs.