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Three men A, B, C working together can do a job in 6 hours less time than A alone, in one 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:
Answer & Solution
Correct Answer:
Option
D
Time taken by A =x hours.
Therefore taken by A, B and C together = (x - 6)
Time taken by B = (x - 5)
Time taken by C = 2(x - 6)
Now, rate of work of A + Rate of work of B + Rate of work of C = Rate of work of ABC.
$$ \Rightarrow \frac{1}{x} + \frac{1}{{x - 5}} + \frac{1}{{2\left( {x - 6} \right)}} = \frac{1}{{x - 6}}$$
On solving above equation, we get x = 3, $$\frac{{40}}{6}$$
When x = 3, the expression (x - 6) becomes negative, thus it's not possible.
$$ \Rightarrow x = \frac{{40}}{6}$$
Time taken by A & B together = $$\frac{1}{{\frac{3}{{20}} + \frac{3}{5}}}$$
= $$\frac{4}{3}$$ hours
On solving above equation, we get x = 3, $$\frac{{40}}{6}$$
When x = 3, the expression (x - 6) becomes negative, thus it's not possible.
$$ \Rightarrow x = \frac{{40}}{6}$$
Time taken by A & B together = $$\frac{1}{{\frac{3}{{20}} + \frac{3}{5}}}$$
= $$\frac{4}{3}$$ hours
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LoginABC=x days
A=x+6 days
B=x+1 days
C=2x days
On solving u get x=2/3 and -3
Read the question carefully ......
x=2/3
A=2/3+6=20/3hrs
B=2/3+1=5/3hrs
a+b=ab/a+b=4/3
therefore time taken by A= (x+6) hour
taken by B= (x+1) hour
and time taken by C= (2x) hour
now, {{1/(x+6)} + {1/(x+1)} + {1/2x}] = 1/x
on solving x=2/3
time taken by A= 2/3 + 6 = 20/3
and time taken by B = 2/3 + 1 = 5/3
work done by (A+B) in 1 hour
1/(20/3) + 1/(5/3) =3/20 + 3/5 = 15/20 =3/4
time taken by (A+B) to complete the work
1/(3/4) = 4/3
If we take x=3 then how will we get 4/3 hrs as answer??
Plz tell....