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01 Aug 2024, 01:30
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B
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64% (02:56) correct
36%
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The days taken to built a wall individually by each of A, B, C, D and E is 20 days, 15 days, 12 days, 10 days and 6 days. They divide themselves into two teams such that the days taken by the two teams to finish the work are in the ratio 1.5 : 4.5. Find the team that finishes earlier.
A. A, B
B. C, D, E
C. B, C
D. A, D, E
E. B, E
A. A, B
B. C, D, E
C. B, C
D. A, D, E
E. B, E
01 Aug 2024, 03:33
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Method 1:
First find the efficiency of A, B, C, D, E.
For that find LCM \((A, B, C, D, E) = lcm(20, 15, 12, 10, 6) = 60\). (Note: this "60" is called total work)
Thus, efficiency of \(A = \dfrac{60}{20}, B = \dfrac{60}{15}, C = \dfrac{60}{12}, D = \dfrac{60}{10} , E = \dfrac{60}{6}\)
\(\implies A = 3, B = 4, C = 5, D = 6, E = 10\)
Now, select from the options and add the efficiency from the above,
\(\text{Total Efficiency} = A + B + C + D + E = 3 + 4 + 5 + 6 + 10 = 28\)
A. A, B = 3 + 4 = 7 (Remaining = 28 - 7 = 21) Ratio = \(\dfrac{7}{21} = \dfrac{1}{3}\) (matches)
B. C, D, E = 5 + 6 + 10 = 21 (Remaining = 28 - 7) Ratio = \(\dfrac{7}{21} = \dfrac{1}{3}\) (matches, Follow NOTE, this is maximum efficiency).
C. B, C = 4 + 5 = 9 (Remaining = 28 - 9 = 19) Ratio = \(\dfrac{9}{19}\)
D. A, D, E = 3 + 6 + 10 = 19 (Remaining = 28 - 19 = 9) Ratio = \(\dfrac{9}{19}\)
E. B, E = 4 + 10 = 14 (Remaining = 28 - 14 = 14) Ratio = \(\dfrac{14}{14} = 1\)
B
First find the efficiency of A, B, C, D, E.
For that find LCM \((A, B, C, D, E) = lcm(20, 15, 12, 10, 6) = 60\). (Note: this "60" is called total work)
Thus, efficiency of \(A = \dfrac{60}{20}, B = \dfrac{60}{15}, C = \dfrac{60}{12}, D = \dfrac{60}{10} , E = \dfrac{60}{6}\)
\(\implies A = 3, B = 4, C = 5, D = 6, E = 10\)
Quote:
The two team may be \(x, y\), and the ratio of the work done is \(\dfrac{x}{y} = \dfrac{1.5}{4.5} = \dfrac{1}{3}\)
Now, select from the options and add the efficiency from the above,
\(\text{Total Efficiency} = A + B + C + D + E = 3 + 4 + 5 + 6 + 10 = 28\)
A. A, B = 3 + 4 = 7 (Remaining = 28 - 7 = 21) Ratio = \(\dfrac{7}{21} = \dfrac{1}{3}\) (matches)
B. C, D, E = 5 + 6 + 10 = 21 (Remaining = 28 - 7) Ratio = \(\dfrac{7}{21} = \dfrac{1}{3}\) (matches, Follow NOTE, this is maximum efficiency).
C. B, C = 4 + 5 = 9 (Remaining = 28 - 9 = 19) Ratio = \(\dfrac{9}{19}\)
D. A, D, E = 3 + 6 + 10 = 19 (Remaining = 28 - 19 = 9) Ratio = \(\dfrac{9}{19}\)
E. B, E = 4 + 10 = 14 (Remaining = 28 - 14 = 14) Ratio = \(\dfrac{14}{14} = 1\)
B
08 Sep 2024, 18:08
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Rate * Time = Work
If Work = 1, then Rate = 1 / Time
Time Taken by A, B,C, D, and E is 20 days, 15 days, 12 days, 10 days and 6 days
=> Rate of A, B, C, D and E will be 1/20, 1/15, 1/12, 1/10, 1/6
Let's make the denominator common for all of them by taking LCM(20,15,12,10,6) = 60
=> Rate of A, B, C, D and E will be 3/60, 4/60, 5/60, 6/60, 10/60
Ratio of time taken by the two teams = 1.5 : 4.5 = 1.5 / 4.5 = 1/3
Now, We need to split A, B, C, D and E intwo two teams such that Sum of rate of all memebers of 1 team = 1/3rd of Sum of rate of all memebers of the other team
Or, Sum of rates of one team = 3 * Sum of rates of other team
Rate of A, B, C, D and E will be 3/60, 4/60, 5/60, 6/60, 10/60
As denominator is same for all and we just need the ratio of the rates so we can ignore the denominator to find the solution
=> Rate of A, B, C, D and E are ~ to 3 , 4, 5, 6, 10
Now, 3 + 4 = 7 and 5 + 6 + 10 = 21 and 21 = 3 * 7
=> Slower team = A and B, Faster team = C, D and E
So, Answer will be B
Hope it Helps!
Watch following video to MASTER Work Rate Problems
If Work = 1, then Rate = 1 / Time
Time Taken by A, B,C, D, and E is 20 days, 15 days, 12 days, 10 days and 6 days
=> Rate of A, B, C, D and E will be 1/20, 1/15, 1/12, 1/10, 1/6
Let's make the denominator common for all of them by taking LCM(20,15,12,10,6) = 60
=> Rate of A, B, C, D and E will be 3/60, 4/60, 5/60, 6/60, 10/60
Ratio of time taken by the two teams = 1.5 : 4.5 = 1.5 / 4.5 = 1/3
Now, We need to split A, B, C, D and E intwo two teams such that Sum of rate of all memebers of 1 team = 1/3rd of Sum of rate of all memebers of the other team
Or, Sum of rates of one team = 3 * Sum of rates of other team
Rate of A, B, C, D and E will be 3/60, 4/60, 5/60, 6/60, 10/60
As denominator is same for all and we just need the ratio of the rates so we can ignore the denominator to find the solution
=> Rate of A, B, C, D and E are ~ to 3 , 4, 5, 6, 10
Now, 3 + 4 = 7 and 5 + 6 + 10 = 21 and 21 = 3 * 7
=> Slower team = A and B, Faster team = C, D and E
So, Answer will be B
Hope it Helps!
Watch following video to MASTER Work Rate Problems
