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