Management Aptitude Test 2017 Paper

(b) 10 min
Let, the full dam is filled by 4 inlets A, B, C and D in w, x, y and z min, respectively.
Dam filled by A, B and C in 1 min
=

1

w

+

1

x

+

1

y

=

1

12

.........(i)
Dam filled by 8, C, and D in 1 min
=

1

x

+

1

y

+

1

z

=

1

15

............(ii)
Dam filled by A and D in 1 min
=

1

w

+

1

z

=

1

20

..............(iii)
From Eqs. (i) and (ii), we get
⇒

1

x

+

1

y

+

1

z

=

1

15

⇒

1

12

−

1

w

+

1

z

=

1

15

[∵

1

x

+

1

y

=

1

12

−

1

w

]
⇒

1

z

−

1

w

=

1

15

−

1

12

=−

1

60

⇒

1

w

−

1

z

=

1

60

...........(iv)
From Eqs (iii) and (iv), we get
w = 30 min and z = 60 min
Again, From Eq. (1),

1

x

+

1

y

=

1

12

−

1

w

⇒

1

x

+

1

y

=

1

12

−

1

30

⇒

1

x

+

1

y

=

5−2

60

=

3

60

⇒

1

x

+

1

y

=

1

20

Now, part of dam filled by the four inlets in 1 min

1

w

+

1

x

+

1

y

+

1

z

=

1

30

+

1

20

+

1

60

=

2+3+1

60

=

6

60

=

1

10

∴ Full dam will be filled by four inlets in 10 min.