Question

Three men A. B and C working together can do a job in 6 hours less time than A alone, in 1 hour less time than B alone and in one half the time needed by C when working alone. Then A and B together can do the job in
(1) 2/3 hrs
(2) 3/4 hrs
(3) 3/2 hrs
(4) 4/3 hrs

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Answer 1

Answer: 4/3 hrs

Step-by-step explanation:Let A, B and C together do the work in x hours.

∴ Time taken by A = (x + 6) hours

Time taken by B = (x + 1) hours

Time taken by C = 2x hours

\therefore \frac{1}{x+6}+\frac{1}{x+1}+\frac{1}{2x} = \frac{1}{x}

=> \frac{1}{x+6}+\frac{1}{x+1} = \frac{1}{x} - \frac{1}{2x} = \frac{1}{2x}

=> \frac{1}{x+6}+\frac{1}{x+1} = \frac{1}{2x}

=> \frac{1}{x+6} = \frac{1}{2x} - \frac{1}{x+1} = \frac{x+1-2x}{2x(x+1)}

=> \frac{1}{x+6} = \frac{1-x}{2x^{2}+2x}

=> 2x^{2}+2x = x + 6 - x^{2} - 6x

=> 3x^{2}+7x-6 = 0

=> 3x^{2}+9x-2x-6 = 0

=> 3x(x+3)-2(x+3) = 0

=> (3x-2)(x+3) = 0

=> 3x - 2 = 0\ as \ x+3 \neq  0

=> x = \frac{2}{3}

∴ Time taken by A = 6+\frac{2}{3} = \frac{18+2}{3} = \frac{20}{3}\ hours

Time taken by B = 1+\frac{2}{3} = \frac{5}{3}\ hours

∴ (A + B)’s 1 day’s work = \frac{3}{20} + \frac{3}{5} = \frac{3+12}{20} = \frac{15}{20} = \frac{3}{4}

∴ Required Time = \frac{4}{3}\ hours

Hence option [D] is correct answer.