Working together B and C take 50% more number of days than A, B and C together take and A and B working together, take $$\frac{8}{3}$$ more number of days than A, B and C take together. If A, B and C all have worked together till the completion of the work and B has received Rs. 120 out of total earnings of Rs. 450, then in how many days did A, B and C together complete the whole work?
A. 2 days
B. 4 days
C. 6 days
D. 8 days
E. 10 days
Answer: Option B
Solution(By Examveda Team)
Ratio of efficiencies of A, B and C,= 5x : 4x : 6x
Number of days required by A and B = $$\frac{{100}}{{9{\text{x}}}}$$ ------ (1)
Number of days required by A, B and C = $$\frac{{100}}{{15{\text{x}}}}$$ ------ (2) $$\eqalign{ & \frac{{100}}{{9{\text{x}}}} - \frac{{100}}{{15{\text{x}}}} = \frac{8}{3} \cr & \Rightarrow {\text{x}} = \frac{5}{3} \cr} $$
Number of days required by A, B and C
= $$\frac{{100}}{{15{\text{x}}}}$$
= $$\frac{{100}}{{15 \times \frac{5}{3}}}$$
= 4 days
This Question Belongs to Arithmetic Ability >> Time And Work
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Related Questions on Time and Work
A. 18 days
B. 24 days
C. 30 days
D. 40 days
If a, b, and c take x days
then b and c take 50% more days
means x + x/2 = 3x/2 days
ratio will be
a+b+c : b+c = x : 3x/2 = 2x : 3x
So ratio off efficiency becomes 3x : 2x
Now, efficiency of A is,
(A + B + C) - (B + C) = 3x - 2x
A = x
So, the efficiency of A is 1/3rd of (A+B+C) [i.e. 1/3 * 3x = x]
Now, share of B given 120 out of 450 = 120/450 = 4/15
We can find ratio of efficiencies now,
A = 1/3 = 5/15
B = 4/15
C = (15-4-5)/15 = 6/15
i.e. 5 : 4 : 6
Now, ratio of number of days = 1/5 : 1/4 : 1/6
=> 60x/5 : 60x/4 : 60x/6
=> 12x : 15x : 10x
Now, One day work of A & B = 1/12x + 1/15x = 9/60x
So, A & B will take 60x/9 days to complete the work.
therefore, A,B & C = 1/12x + 1/15x + 1/10x = 15/60x
So, A,B & C will take 60x/15 days to complete the work.
Now given that A and B take 8/3 days more than A, B and C
So, 60x/9 - 60x/15 = 8/3
Solving this we get x = 1
Thus number of days A, B and C will take to complete the whole work is 60x/15 = 4x = 4*1 = 4days.
12/18=2/3
1-2/3=1/3
Then whole work completed by B is = 3*15=45
A's part= 1/18-1/45=1/30
A:B= 30:45=2:3
then A's share= 1500*2/5=600
Let say A , B & C takes A , B & C days respectively to complete the work
=> A , B & C 's 1 day work = 1/A , 1/B & 1/C respectively
B& C complete work in 1/(1/B + 1/C)
A B & C complete work in 1/(1/A + 1/B + 1/C)
1/(1/B + 1/C) = 1/(1/A + 1/B + 1/C) * (3/2)
=> 2(1/A + 1/B + 1/C) = 3(1/B + 1/C)
=> 2/A = 1/B + 1/C
1/A + 1/B + 1/C = 1/A + 2/A = 3/A
Time taken to complete work together by A , B & C = A/3
work done by B in A/3 days = A/3B
=> A/3B = 120/450
=> 5A = 4B
1/(1/A + 1/B) = A/3 + 8/3
=> 1/(1/A + 4/5A) + A/3 + 8/3
=> 5A/9 = A/3 + 8/3
=> 5A = 3A + 24
=> 2A = 24
=> A = 12
answear is 4 days then how is 8 days
how was the ratio calculated here?
How we find the ratio of efficiency, please reply.