CBSE Class 10 Answered

"Two water taps together can fill a tank in hours."

So we assume you meant it takes an hour for two taps together to fill the tank.

V - volume of tank, v₁ - flow rate from tap 1, v₂ - flow rate from tap 2

Time = Volume/Flow rate.

For tap 1,

T₁ = V/v₁

Similarly for tap 2,

T₂ = V/v₂

Two taps together,

1 hr = V/(v₁+v₂) = 1/(v₁/V + v₂/V) = 1/(1/T₁ + 1/T₂)

T₂ = T₁ + 10   ........

1 hr = 1/(1/T₁ + 1/(T₁+10))

1 = T₁(T₁+10)/(T₁ + T₁+10)

T₁² + 8T₁ - 10 = 0.

T₁ = [-8±(64+40)]/2

= 1.099 hr .......and we reject other root since time can't be negative.

T₂ = 11.099 hr.

The time required by large diameter tap is 1.099 hr or 1 hr 6 min and required by small diameter tap is,

11 hrs 6 min.

Regards,

Team,

TopperLearning.