Question

One tank can be filled up by two taps in 6 hours. The smaller tap alone takes 5 hours more than the bigger tap alone. Find the time required by each tap to fill the tank separately. ​​

Answer 1

Explanation:

Let time taken to fill tank by small tap be x hours

Time taken to fill tank by big tap be y hours

Then, x−y=5 or x=5+y

Smaller tap can fill in one hour =

x

1

Bigger tap can fill in one hour =

y

1

Then,

x

1

+

y

1

=

6

1

xy

x+y

=

6

1

xy=6(x+y)

y(5+y)=6(5+y+y)

5y+y

2

=30+12y

y

2

−7y−30=0

y=

2

7±

49+120

y=

2

7±13

y=10,−3

x=5+10=5+10=15 hours

Hence, Small tap can fill the tank in 15 hours and bigger tap can fill in 10 hours