Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 16)
16.
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
Answer: Option
Explanation:
| Work done by X in 4 days = |  |
1 | x 4 |  |
= | 1 | . |
| 20 | 5 |
| Remaining work = | |
1 - | 1 | |
= | 4 | . |
| 5 | 5 |
| (X + Y)'s 1 day's work = | |
1 | + | 1 | |
= | 8 | = | 2 | . |
| 20 | 12 | 60 | 15 |
| Now, | 2 | work is done by X and Y in 1 day. |
| 15 |
| So, | 4 | work will be done by X and Y in | |
15 | x | 4 | |
= 6 days. |
| 5 | 2 | 5 |
Hence, total time taken = (6 + 4) days = 10 days.
Discussion:
68 comments Page 5 of 7.
Deepak Patgar said:
1 decade ago
Chocolate method:
LCM of 20 and 12 is 60. there are 60 chocolates and.
A requires 20 days to eat 60 chocolates. He eats 3 chocolates per day.
B requires 12 days to eat 60 chocolates. He eats 5 chocolates per day.
For the first 4 days A alone eats the chocolates. total number of chocolates eaten up by A in 4 days is 12.
Remaining chocolates are (60-12) = 48.
A and B together eats 8 chocolates per day.
So to eat 48 chocolates they will need 48/8 = 6 days.
Total number of days = 4+6 = 10.
LCM of 20 and 12 is 60. there are 60 chocolates and.
A requires 20 days to eat 60 chocolates. He eats 3 chocolates per day.
B requires 12 days to eat 60 chocolates. He eats 5 chocolates per day.
For the first 4 days A alone eats the chocolates. total number of chocolates eaten up by A in 4 days is 12.
Remaining chocolates are (60-12) = 48.
A and B together eats 8 chocolates per day.
So to eat 48 chocolates they will need 48/8 = 6 days.
Total number of days = 4+6 = 10.
Aakash said:
1 decade ago
x+4/20+x/12 = 1.
3(x+4)+5(x)/60 = 1.
3x+12+5x = 60.
8x+12 = 60.
8x = 60-12.
8x = 48.
x = 6.
i.e., x+4 = 6+4.
10 days.
3(x+4)+5(x)/60 = 1.
3x+12+5x = 60.
8x+12 = 60.
8x = 60-12.
8x = 48.
x = 6.
i.e., x+4 = 6+4.
10 days.
Amarnath said:
1 decade ago
Sorry @Zia Don't apply formulas it loses confidence for others. Whatever they know will apply if try tell in simple answer don't tell with formulas.
Zia said:
1 decade ago
Hi, I have a shortcut.
(X-a)*Y/X+Y [X=20,Y=12,a=4]
= (20-4)*12/20+12.
= 16*12/32.
= 12/2.
= 6.
So, total time taken (6+4) = 10 days.
(X-a)*Y/X+Y [X=20,Y=12,a=4]
= (20-4)*12/20+12.
= 16*12/32.
= 12/2.
= 6.
So, total time taken (6+4) = 10 days.
Kavya said:
1 decade ago
Short cut: A=20, B=12.
4 days left: 20-4 = 16.
B joined : (1/20) + (1/12) = 15/2.
Therefore: (16/20)(15/2) = 6.
Total days = 6+4 = 10.
4 days left: 20-4 = 16.
B joined : (1/20) + (1/12) = 15/2.
Therefore: (16/20)(15/2) = 6.
Total days = 6+4 = 10.
(1)
Padma said:
1 decade ago
A+B can work
1/20+1/12=8/60.
A can work =4*1/20=1/5.
Remaining work=1-1/5=4/5.
A+B work to days 1/n formula=60/8.
60/8*4/5=6 days.
Total day taken will be=6+4=10.
1/20+1/12=8/60.
A can work =4*1/20=1/5.
Remaining work=1-1/5=4/5.
A+B work to days 1/n formula=60/8.
60/8*4/5=6 days.
Total day taken will be=6+4=10.
Ashish said:
1 decade ago
Work done by A in 1 day=1/20.
Work done by B in 1 day=1/12.
(A+B) 'S 1 DAY WORK=1/20+1/12=8/60.
So A can work in 4 days =4*1/20=1/5.
So remaining work=1-1/5=4/5.
So 4/5 of work done by (A+B) =4/5*60/8.
=6 DAYS.
TOTAL DAY TAKEN WILL BE=6+4=10 DAYS.
Work done by B in 1 day=1/12.
(A+B) 'S 1 DAY WORK=1/20+1/12=8/60.
So A can work in 4 days =4*1/20=1/5.
So remaining work=1-1/5=4/5.
So 4/5 of work done by (A+B) =4/5*60/8.
=6 DAYS.
TOTAL DAY TAKEN WILL BE=6+4=10 DAYS.
ANURAG said:
1 decade ago
(x and y)'s one day work= 2/15
Therefore total number of days for the total work= 15/2
And,total number of days for 4/5 of the work=( 15/2 )*(4/5)
Hence total time = 6+4 = 10 days
Therefore total number of days for the total work= 15/2
And,total number of days for 4/5 of the work=( 15/2 )*(4/5)
Hence total time = 6+4 = 10 days
Shro said:
1 decade ago
6+4 =10
Is here 4 takes from the question? " X started the work alone and then after 4 days"
Is here 4 takes from the question? " X started the work alone and then after 4 days"
Mahesh said:
1 decade ago
1day per x work as = 1/20 && y= 1/12..
x do work 4days ..then 4*1/20=1/5 then remaining work= 1-1/5=4/5
Remaining work's done by y i.e. 1work ---> 12
4/5 ------> x
x=4/5 * 12 = 48/5 = 9.6day nearly = 10days..
It's good method to understand GUYS..!
x do work 4days ..then 4*1/20=1/5 then remaining work= 1-1/5=4/5
Remaining work's done by y i.e. 1work ---> 12
4/5 ------> x
x=4/5 * 12 = 48/5 = 9.6day nearly = 10days..
It's good method to understand GUYS..!
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers