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03 Feb 2021, 05:45
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Four friends P, Q, R and S are working on an assignment together. They contribute to the work in 4 the ratio 1:2:3:4, respectively. They can complete the assignment individually in 1, 2, 3 and 4 days, respectively. If they work one after the other, how many days will it take to complete the assignment?
(A) 3 days
(B) 3 1/4 days
(C) 3 1/2 days
(D) 4 days
(E) 4 1/2 days
(A) 3 days
(B) 3 1/4 days
(C) 3 1/2 days
(D) 4 days
(E) 4 1/2 days
03 Feb 2021, 12:04
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Work-Rate Problem
Since the time taken by the four friends to complete the same task individually is 1, 2, 3 and 4 days, respectively so it will be easier to solve the problem is work done is taken as a LCM of (1,2,3,4) * Sum of ratio (1,2,3,4)= 12 * 10 = 120
Using Rate * Time = Work done we can find rate of P,Q,R,S
Calculate Rate
Let rate of P,Q,R,S be P,Q,R,S respectively
P * time = work done
=> P * 1 = 120 => P = \(\frac{120}{1}\) = 120
Similarly, Q = \(\frac{120}{2}\) = 60
R = \(\frac{120}{3}\) = 40
S = \(\frac{120}{4}\) = 30
Calculate Work
Work done by each of them is in the ratio 1:2:3:4, respectively => it is in the ratio \(\frac{1}{10}\):\(\frac{2}{10}\):\(\frac{3}{10}\):\(\frac{4}{10}\)
=> Actual work done by P,Q,R,S can be calculated by multiplying total work (120) by these fractions
=> Work done by P = \(\frac{1}{10}\) * 120 = 12
=> Work done by Q = \(\frac{2}{10}\) * 120 = 24
=> Work done by R = \(\frac{3}{10}\) * 120 = 36
=> Work done by S = \(\frac{4}{10}\) * 120 = 48
Calculate Time
Time taken by all of them to finish the work in sequence (one after the other ) = Time taken by each one of them to finish their part of work
= Time Taken by P + Time Taken by Q + Time Taken by R + Time Taken by S
= \(\frac{12}{120}\) + \(\frac{24}{60}\) + \(\frac{36}{40}\) + \(\frac{48}{30}\)
= \(\frac{12}{120}\) + \(\frac{48}{120}\) + \(\frac{108}{120}\) + \(\frac{192}{120}\)
= \(\frac{360}{120}\) = 3 days
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Solve Work Rate Problems
Since the time taken by the four friends to complete the same task individually is 1, 2, 3 and 4 days, respectively so it will be easier to solve the problem is work done is taken as a LCM of (1,2,3,4) * Sum of ratio (1,2,3,4)= 12 * 10 = 120
Using Rate * Time = Work done we can find rate of P,Q,R,S
Calculate Rate
Let rate of P,Q,R,S be P,Q,R,S respectively
P * time = work done
=> P * 1 = 120 => P = \(\frac{120}{1}\) = 120
Similarly, Q = \(\frac{120}{2}\) = 60
R = \(\frac{120}{3}\) = 40
S = \(\frac{120}{4}\) = 30
Calculate Work
Work done by each of them is in the ratio 1:2:3:4, respectively => it is in the ratio \(\frac{1}{10}\):\(\frac{2}{10}\):\(\frac{3}{10}\):\(\frac{4}{10}\)
=> Actual work done by P,Q,R,S can be calculated by multiplying total work (120) by these fractions
=> Work done by P = \(\frac{1}{10}\) * 120 = 12
=> Work done by Q = \(\frac{2}{10}\) * 120 = 24
=> Work done by R = \(\frac{3}{10}\) * 120 = 36
=> Work done by S = \(\frac{4}{10}\) * 120 = 48
Calculate Time
Time taken by all of them to finish the work in sequence (one after the other ) = Time taken by each one of them to finish their part of work
= Time Taken by P + Time Taken by Q + Time Taken by R + Time Taken by S
= \(\frac{12}{120}\) + \(\frac{24}{60}\) + \(\frac{36}{40}\) + \(\frac{48}{30}\)
= \(\frac{12}{120}\) + \(\frac{48}{120}\) + \(\frac{108}{120}\) + \(\frac{192}{120}\)
= \(\frac{360}{120}\) = 3 days
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Solve Work Rate Problems
Lord_Biplab
Joined: 27 May 2024
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30 Jun 2024, 03:28
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Rates of a, b, c and d = \(\frac{1}{1}\), \(\frac{1}{2}\), \(\frac{1}{3}\) and \(\frac{1}{4}\), respectively.
Contribution to work by each individuals:
A = \(\frac{1}{(1+2+3+4)}\) = \(\frac{1}{10}\)
B = \(\frac{2}{(1+2+3+4)}\) = \(\frac{2}{10}\)
C = \(\frac{3}{(1+2+3+4)}\) = \(\frac{3}{10}\)
D = \(\frac{4}{(1+2+3+4)}\) = \(\frac{4}{10}\)
We know that,
\(Time\) = \(\frac{Work}{Rate}\)
Time taken by A = Work done by A/Rate of A = \(\frac{1}{10}\)/\(\frac{1}{1}\) = \(\frac{1}{10}\)
Time taken by B = Work done by B/Rate of B = \(\frac{2}{10}\) / \(\frac{1}{2}\) = \(\frac{4}{10}\)
Time taken by C = Work done by C/Rate of C = \(\frac{3}{10}\) / \(\frac{1}{3}\) = \(\frac{9}{10}\)
Time taken by D = Work done by D/Rate of D = \(\frac{4}{10}\) / \(\frac{1}{4}\) = \(\frac{16}{10}\)
Total time taken = \(\frac{1}{10}\) + \(\frac{4}{10}\) + \(\frac{9}{10}\) + \(\frac{16}{10}\) = \(3\) \(days\)
Thus, answer is \(A\).
Contribution to work by each individuals:
A = \(\frac{1}{(1+2+3+4)}\) = \(\frac{1}{10}\)
B = \(\frac{2}{(1+2+3+4)}\) = \(\frac{2}{10}\)
C = \(\frac{3}{(1+2+3+4)}\) = \(\frac{3}{10}\)
D = \(\frac{4}{(1+2+3+4)}\) = \(\frac{4}{10}\)
We know that,
\(Time\) = \(\frac{Work}{Rate}\)
Time taken by A = Work done by A/Rate of A = \(\frac{1}{10}\)/\(\frac{1}{1}\) = \(\frac{1}{10}\)
Time taken by B = Work done by B/Rate of B = \(\frac{2}{10}\) / \(\frac{1}{2}\) = \(\frac{4}{10}\)
Time taken by C = Work done by C/Rate of C = \(\frac{3}{10}\) / \(\frac{1}{3}\) = \(\frac{9}{10}\)
Time taken by D = Work done by D/Rate of D = \(\frac{4}{10}\) / \(\frac{1}{4}\) = \(\frac{16}{10}\)
Total time taken = \(\frac{1}{10}\) + \(\frac{4}{10}\) + \(\frac{9}{10}\) + \(\frac{16}{10}\) = \(3\) \(days\)
Thus, answer is \(A\).
