Aptitude - Pipes and Cistern - Discussion

Time taken by 1 tap to fill half of the tank is =3hrs.
part filled by 4 taps in 1 hr=4*1/6=2/3.
then remaining part= 1-2/3=1/3 how is it 1/2 can anybody please tell
and what this ::symbol mean

:: is the sign of proportionality

a,b,c,d=pipes 6 hrs time
a is taken=3 hrs time
a+a+b+c=3hrs each one taken 45 min
final 3hrs+45min

How you write 45min lekha please can you explain me the logic, Im not getting it.

Can anybody explain ths clearly?

Given A tap can fill a tank in 6 hours.

After half the tank is filled i.e. after 3 hrs.

three more similar taps are opened i.e.

no. of taps to fill remaining half tank = 4 taps

when 1 tap is used = (3 hrs/1 tap)

when 4 taps are used = (3 hrs/4 taps)=45min

total= 3hrs+45min

NOTE:
1 tap takes 6hours....now by using four similar such taps it take 3/2 hours to fill the tank......
since all of them are capable of filling the tank in 6 hours)therefore they share time equally----6hours/4taps=3/2 hours )

now lets go to the solution:::

to fill half of the tank...only one tap is used...therefore it takes 3hours.
now 3 more similar taps are used...means now we are using 4 taps which are of same kind..
as explained above..
to fill the tank by the use of four taps----it takes 3/2 hours
now what we require is just to fill the half of the tank
it takes 3/4 hours i.e [3/2]/[1/2]=3/4
threfore we get---3+3/4 means 3 hours 45 min

Can any one explain clearly this ?

@MANASA

How can you write [3/2]/[1/2]= 3/4 ?
Its 3 not 3/4.

How can we write 2/3:1/2::1:x?