Question

Two taps T_(1) and T_(2) can fill a tank in 2 and 3 hrs respectively.If both the taps are opened together the tank gets filled in (a) 2(1)/(2) hrs (b) 1(1)/(2) hrs (c) 1(1)/(4) hrs (d) 1(1)/(5) hrs​

Answer 1

Given : Two taps T_(1) and T_(2) can fill a tank in 2 and 3 hrs respectively.

both the taps are opened together

To Find : Time taken for the tank gets filled  

Solution:

Tap 1 can fill  tank in  2 hrs

Tap 1 can fill in 1hr  =  1/2

Tap 2 can fill  tank in  2 hrs

Tap 2 can fill in 1hr  =  1/3

Both taps together can fill in 1 hr

= 1/2 + 1/3

= ( 5/6)

Hence bot taps can fill the tank in 1/(5/6)   = 6/5 hrs

= 1  1/5 hrs

= $1\frac{1}{5} \text{ hrs}$

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Answer 2

Solution :-

LCM of 2 and 3 = 6 units = Let capacity of tank .

so,

→ Efficiency of Tape T(1) = Total capacity / Total time = 6/2 = 3 units / hour .

and,

→ Efficiency of Tape T(2) = Total capacity / Total time = 6/3 = 2 units / hour .

then,

→ Efficiency of T(1) + T(2) = 3 + 2 = 5 units / hour .

therefore,

→ Time taken by both taps to fill the tank = Total capacity / Total efficiency = (6/5) = 1(1/5) hours (d) (Ans.)

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