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

Answer:

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

Answer 2

Step-by-step explanation:

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. ... The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.