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:
A. $$\frac{2}{3}$$ hours
B. $$\frac{3}{4}$$ hours
C. $$\frac{3}{2}$$ hours
D. $$\frac{4}{3}$$ hours
Answer: Option D
Solution(By Examveda Team)
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
This Question Belongs to Arithmetic Ability >> Time And Work
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Comments ( 14 )
Related Questions on Time and Work
A. 18 days
B. 24 days
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How u get the value of x
4/3 hoga Ans
Most of them posted wrong answers ......
ABC=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 ......
Ser ye 2/3 kese aaya please explain
3/4 hr hi h Ans.
or,1/x=(1/x+6)+(1/x+1)+(1/2x)
x=2/3
A=2/3+6=20/3hrs
B=2/3+1=5/3hrs
a+b=ab/a+b=4/3
@Bhanu Kya Aap explain karenge kyo 3/4 hoga?
3/4hr hona chahiye ans
Your Comment...ans will be 3/4
4/3...3/4 to efficiency ha bhanu dyani bhai
Because,There has been given that C take half time than B.
why take c= twice of b?
Let time taken by A,B and C when working together is x hour
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
Sir, i couldn't get the last step??
If we take x=3 then how will we get 4/3 hrs as answer??
Plz tell....