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29 Jan 2026, 05:55
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
72% (03:34) correct
28%
(03:32)
wrong
based on 96
sessions
History
Date
Time
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Shantel, Rayaan, Ronald and Alfie work in a company where manufacturing and packing of biscuits is done. Shantel can fill a large carton of biscuits in 5 hours, and Rayaan can fill the same carton in 20 hours. Ronald can empty the full carton in 10 hours and Alfie can empty the carton in 40 hours. If Shantel starts work, and Ronald joins Shantel after 2 hours, and Rayaan joins them after 2 more hours, and Alfie joins them after 2 more hours, then after how many hours will the cartoon be completely filled?
A. 22/5
B. 29/5
C. 34/5
D. 43/5
C. 48/5
A. 22/5
B. 29/5
C. 34/5
D. 43/5
C. 48/5
31 Jan 2026, 23:03
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Let the work required to fill or empty the full carton be W.
Let the rate of work of Shantel be Rs, that of Rayaan be Rra, Ronald be Rro and that of Alfie be Ra.
Thus,
Rs = W/5
Rra = W/20
Rro = -W/10
Ra = -W/40
For ease of calculation, let the work W = LCM of the time taken by each of them = LCM(5,20,10,40) = 40
Hence, we get:
Rs = 8
Rra = 2
Rro = -4
Ra = -1
Let's now frame an equation for the work done according to the conditions given in the question:
Work done by Shantel in 2 hours = 2*8 = 16 (as Work = Rate*Time)
Work done by Ronald and Shantel in 2 hours = 2*(8-4) = 8
Work done by Ronald, Shantel and Rayaan in 2 hours = 2*(8-4+2) = 12
Work done by them all in 't' hours = t*(8+2-4-1) = 5t
Hence, 16+8+12+5t = 40
Thus, t = 4/5
Total time required = 4/5 + 2*3 = 34/5 hours
Hence, the correct answer is Option C - 34/5.
Let the rate of work of Shantel be Rs, that of Rayaan be Rra, Ronald be Rro and that of Alfie be Ra.
Thus,
Rs = W/5
Rra = W/20
Rro = -W/10
Ra = -W/40
For ease of calculation, let the work W = LCM of the time taken by each of them = LCM(5,20,10,40) = 40
Hence, we get:
Rs = 8
Rra = 2
Rro = -4
Ra = -1
Let's now frame an equation for the work done according to the conditions given in the question:
Work done by Shantel in 2 hours = 2*8 = 16 (as Work = Rate*Time)
Work done by Ronald and Shantel in 2 hours = 2*(8-4) = 8
Work done by Ronald, Shantel and Rayaan in 2 hours = 2*(8-4+2) = 12
Work done by them all in 't' hours = t*(8+2-4-1) = 5t
Hence, 16+8+12+5t = 40
Thus, t = 4/5
Total time required = 4/5 + 2*3 = 34/5 hours
Hence, the correct answer is Option C - 34/5.
01 Feb 2026, 14:33
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Let's solve this algebraically via our basic formula here i.e., A=RT or R=A/T
So, given the info, following are the rates of the 4 individuals mentioned :
To fill:
Shantel = 1/5
Rayaan = 1/20
and, To empty:
Ronald = 1/10
Alfie = 1/40
Let's go step by step
Given: Shantel worked initially for 2 hours and hence total work done by him
A=RT : (1/5)x2 = (2/5)
After 2 hours, Ronald joins in and together the amount they will get done in 2 hours:
(1/5-1/10)x2 = (1/5)
(Note: We have to subtract the Ronald's rate from Shantel's since one is filling the cartons and another is emptying them)
After 2 hours, Rayaan joins them to work for another 2 hours:
(1/5 + 1/20 - 1/10) x 2 = (3/10)
Now, we can finally accumulate the total work done till now and accordingly find out what will remain to be done when Alfie joins them three:
So, lets add our work till now : (2/5)+(1/5)+(3/10) = (9/10), meaning we only have (1/10) of the amount of work remaining.
With Alfie joining them, their final combined rate would be = (1/5)+(1/20)-(1/10)-(1/40) = (1/8)
Now, we have our R=(1/8), A=(1/10), we can now find out the time =
T=A/R = (1/10)/(1/8) = 4/5 hours
However, we also need to add the hours worked by Shantel, Ronald and Rayaan i.e. (2+2+2) = 6 hours
Conclusively, total time = 6+(4/5) = (34/5). Option C.
So, given the info, following are the rates of the 4 individuals mentioned :
To fill:
Shantel = 1/5
Rayaan = 1/20
and, To empty:
Ronald = 1/10
Alfie = 1/40
Let's go step by step
Given: Shantel worked initially for 2 hours and hence total work done by him
A=RT : (1/5)x2 = (2/5)
After 2 hours, Ronald joins in and together the amount they will get done in 2 hours:
(1/5-1/10)x2 = (1/5)
(Note: We have to subtract the Ronald's rate from Shantel's since one is filling the cartons and another is emptying them)
After 2 hours, Rayaan joins them to work for another 2 hours:
(1/5 + 1/20 - 1/10) x 2 = (3/10)
Now, we can finally accumulate the total work done till now and accordingly find out what will remain to be done when Alfie joins them three:
So, lets add our work till now : (2/5)+(1/5)+(3/10) = (9/10), meaning we only have (1/10) of the amount of work remaining.
With Alfie joining them, their final combined rate would be = (1/5)+(1/20)-(1/10)-(1/40) = (1/8)
Now, we have our R=(1/8), A=(1/10), we can now find out the time =
T=A/R = (1/10)/(1/8) = 4/5 hours
However, we also need to add the hours worked by Shantel, Ronald and Rayaan i.e. (2+2+2) = 6 hours
Conclusively, total time = 6+(4/5) = (34/5). Option C.
Amity007
