A takes 6 days less than …
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Sia ? 6 years, 6 months ago
Let B takes x days to finish the work, then A alone can finish it in (x - 6) days
According to question,
{tex}\frac { 1 } { x } + \frac { 1 } { x - 6 } = \frac { 1 } { 4 }{/tex}
{tex}\Rightarrow \frac { x - 6 + x } { x ^ { 2 } - 6 x } = \frac { 1 } { 4 }{/tex}
{tex}\Rightarrow \frac { 2 x - 6 } { x ^ { 2 } - 6 x } = \frac { 1 } { 4 }{/tex}
{tex}\Rightarrow{/tex} x2 - 6x = 8x - 24
{tex}\Rightarrow{/tex} x2 - 14x + 24 = 0
{tex}\Rightarrow{/tex} x2 - 12x - 2x + 24 = 0
{tex}\Rightarrow{/tex} x(x - 12) - 2(x - 12) = 0
{tex}\Rightarrow{/tex} (x - 12)(x - 2) = 0
{tex}\Rightarrow{/tex} x = 12 or x = 2
x = 2 (Neglect as A's days can't be negative)
So, B takes x = 12 days.
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