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02 Dec 2020, 13:00
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
65% (03:13) correct
35%
(03:23)
wrong
based on 203
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A does a work in 90 days, B in 40 days and C in 12 days. They work one after another for a day each, starting with A followed by B and then by C. If the total amount received is $360 and A, B, and C share it in the ratio of the work done. What is their respective individual wages?
A. A = 40, B = 60 and C = 260
B. A = 36, B = 81 and C = 243
C. A = 42, B = 86 and C = 232
D. A = 38, B = 88 and C = 234
E. A = 36, B = 90 and C = 234
A. A = 40, B = 60 and C = 260
B. A = 36, B = 81 and C = 243
C. A = 42, B = 86 and C = 232
D. A = 38, B = 88 and C = 234
E. A = 36, B = 90 and C = 234
02 Dec 2020, 14:11
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[b]CONCEPT:[/b] Time and Work
Wages are paid in the proportion of work done.
SOLUTION: Let total work be 360units(LCM 40,60,12)
Thus efficiencies of A,B,C are 360/90,360/40,12=4,9,30 units respectively or43 units together in a day(4+9+30)
Total work in 24 days=43*8=344 units[Every 3 days 43 units of work is done and 344 is the nearest number to 360 as a multiple of43]
In the next two days(25th and 26th) 4+9=13 units of work is completed by A and B respectively.
By now 344+13=357 units of work has been done
Remaining work =360-357=3 units
This at the rate of 30units a day is completed by C in 3/30=1/10th of the 27th day.
Hence A&B worked for 9 days each and completed 9*4=36 and 9*9=81units of work respectively.
Total work A & B completed is 36+81=117units.
Rest of the work(360-117)=243 units is done by C alone.
Wages shall also be distributed in the ratio of work done which is 36,81,243 (B)
Hope this helps.
Devmitra Sen
Wages are paid in the proportion of work done.
SOLUTION: Let total work be 360units(LCM 40,60,12)
Thus efficiencies of A,B,C are 360/90,360/40,12=4,9,30 units respectively or43 units together in a day(4+9+30)
Total work in 24 days=43*8=344 units[Every 3 days 43 units of work is done and 344 is the nearest number to 360 as a multiple of43]
In the next two days(25th and 26th) 4+9=13 units of work is completed by A and B respectively.
By now 344+13=357 units of work has been done
Remaining work =360-357=3 units
This at the rate of 30units a day is completed by C in 3/30=1/10th of the 27th day.
Hence A&B worked for 9 days each and completed 9*4=36 and 9*9=81units of work respectively.
Total work A & B completed is 36+81=117units.
Rest of the work(360-117)=243 units is done by C alone.
Wages shall also be distributed in the ratio of work done which is 36,81,243 (B)
Hope this helps.
Devmitra Sen
General Discussion
02 Dec 2020, 13:53
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Good question Bunuel
Sharing my solution below-
The approach to solving this question would be-
1. Identify the amount of work completed by all of them together (in 3 days, since they are not working simultaneously, but one after another)
2. Calculate the number of days taken in all to complete the work
3. Identify the ratio of work done by each one of them
4. Divide the payment received by them in the ratio of the work done by them
A completes 1/90 work in 1 day (on Day 1)
B completes 1/40 work in 1 day (on Day 2)
C completes 1/12 work in 1 day (on Day 3)
Together they complete 43/360 work together in 3 days
So in 24 days, they complete (43*8)/360 work= 344/360 work= 43/45 work
Remaining work left= 2/45= 4/90 work
On the 25th day, A will work again and complete 1/90 work.
Remaining work= 4/ 90- 1/90= 3/90 work
On the 26th day, B will work and complete 1/40 work.
Remaining work= 3/ 90- 1/40= 1/120 work
On the 27th day, C will complete the work
C takes to complete 1 work= 12 days
Hence, C takes to complete 1/120 work= 12 * 1/120 day= 1/10 day
So total days taken= 26+1/10 days
Now, lets identify the work done by all three (ratio of work)=
A worked for 9 days
B worked for 9 days
C worked for 8+1/10 days
Ratio of work done by A:B:C= 9*1/90 : 9*1/40 : 81/10*1/12 = 1/10 : 9/40 : 27/40= 4:9:27
Total payment made to them= $360
Let's divide the money in the same ratio as work done to arrive at the answer=
A:B:C= 4/40*360 : 9/40*360 : 27/40*360= 36:81:243 (Answer-- Option B)
Sharing my solution below-
The approach to solving this question would be-
1. Identify the amount of work completed by all of them together (in 3 days, since they are not working simultaneously, but one after another)
2. Calculate the number of days taken in all to complete the work
3. Identify the ratio of work done by each one of them
4. Divide the payment received by them in the ratio of the work done by them
A completes 1/90 work in 1 day (on Day 1)
B completes 1/40 work in 1 day (on Day 2)
C completes 1/12 work in 1 day (on Day 3)
Together they complete 43/360 work together in 3 days
So in 24 days, they complete (43*8)/360 work= 344/360 work= 43/45 work
Remaining work left= 2/45= 4/90 work
On the 25th day, A will work again and complete 1/90 work.
Remaining work= 4/ 90- 1/90= 3/90 work
On the 26th day, B will work and complete 1/40 work.
Remaining work= 3/ 90- 1/40= 1/120 work
On the 27th day, C will complete the work
C takes to complete 1 work= 12 days
Hence, C takes to complete 1/120 work= 12 * 1/120 day= 1/10 day
So total days taken= 26+1/10 days
Now, lets identify the work done by all three (ratio of work)=
A worked for 9 days
B worked for 9 days
C worked for 8+1/10 days
Ratio of work done by A:B:C= 9*1/90 : 9*1/40 : 81/10*1/12 = 1/10 : 9/40 : 27/40= 4:9:27
Total payment made to them= $360
Let's divide the money in the same ratio as work done to arrive at the answer=
A:B:C= 4/40*360 : 9/40*360 : 27/40*360= 36:81:243 (Answer-- Option B)
