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
= $\frac{1}{\mathit{w}}+\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}=\frac{1}{12}$ .........(i)
Dam filled by 8, C, and D in 1 min
= $\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}+\frac{1}{\mathit{z}}=\frac{1}{15}$ ............(ii)
Dam filled by A and D in 1 min
= $\frac{1}{\mathit{w}}+\frac{1}{\mathit{z}}=\frac{1}{20}$ ..............(iii)
From Eqs. (i) and (ii), we get
⇒ $\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}+\frac{1}{\mathit{z}}=\frac{1}{15}$
⇒ $\frac{1}{12}-\frac{1}{\mathit{w}}+\frac{1}{\mathit{z}}=\frac{1}{15}$
$\left[\because \frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}=\frac{1}{12}-\frac{1}{\mathit{w}}\right]$
⇒ $\frac{1}{\mathit{z}}-\frac{1}{\mathit{w}}=\frac{1}{15}-\frac{1}{12}=-\frac{1}{60}$
⇒ $\frac{1}{\mathit{w}}-\frac{1}{\mathit{z}}=\frac{1}{60}$ ...........(iv)
From Eqs (iii) and (iv), we get
w = 30 min and z = 60 min
Again, From Eq. (1),
$\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}=\frac{1}{12}-\frac{1}{\mathit{w}}$
⇒ $\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}=\frac{1}{12}-\frac{1}{30}$
⇒ $\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}=\frac{5-2}{60}=\frac{3}{60}$
⇒ $\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}=\frac{1}{20}$
Now, part of dam filled by the four inlets in 1 min
$\frac{1}{\mathit{w}}+\frac{1}{\mathit{x}}+\frac{1}{\mathit{y}}+\frac{1}{\mathit{z}}$ = $\frac{1}{30}+\frac{1}{20}+\frac{1}{60}$
= $\frac{2+3+1}{60}$ = $\frac{6}{60}=\frac{1}{10}$
∴ Full dam will be filled by four inlets in 10 min.