Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 8)
8.
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
Answer: Option
Explanation:
| (A + B)'s 1 day's work = | 1 |
| 10 |
| C's 1 day's work = | 1 |
| 50 |
| (A + B + C)'s 1 day's work = |  |
1 | + | 1 |  |
= | 6 | = | 3 | . .... (i) |
| 10 | 50 | 50 | 25 |
A's 1 day's work = (B + C)'s 1 day's work .... (ii)
| From (i) and (ii), we get: 2 x (A's 1 day's work) = | 3 |
| 25 |
 A's 1 day's work = |
3 | . |
| 50 |
 B's 1 day's work |
|
1 | - | 3 | |
= | 2 | = | 1 | . |
| 10 | 50 | 50 | 25 |
So, B alone could do the work in 25 days.
Discussion:
146 comments Page 10 of 15.
Venkataramireddy said:
8 years ago
1 day work A+B=1/10.
A can do work same as do B+C.
so we can write it as
A=B+C.....
C 1day work =1/50,
1-day work of A+B+C=1/10+1/50
LCM 50.
5+1/50=6/50=3/25;
A+B+C=3/25,
above B+C=A.
So
A+A=3/25.
2A=3/25,
A=3/50,
substitute A value in A+B=1/10.
3/50+B=1/10,
B=1/10-3/50,
lcm 50,
B=5-3/50,
=2/50,
B=1/25,
B Alone 25 days.
A can do work same as do B+C.
so we can write it as
A=B+C.....
C 1day work =1/50,
1-day work of A+B+C=1/10+1/50
LCM 50.
5+1/50=6/50=3/25;
A+B+C=3/25,
above B+C=A.
So
A+A=3/25.
2A=3/25,
A=3/50,
substitute A value in A+B=1/10.
3/50+B=1/10,
B=1/10-3/50,
lcm 50,
B=5-3/50,
=2/50,
B=1/25,
B Alone 25 days.
PRAVEEN. P said:
8 years ago
A+B=1/10.
C=1/50.
A+B+C=6/50.
But A=B+C.
B+C+B+C=6/50.
2B+2C=6/50.
But C=1/50.
On substitute c in above eqn we get as,
2B=4/50 and,
B=1/25,
Hence B=25 days.
C=1/50.
A+B+C=6/50.
But A=B+C.
B+C+B+C=6/50.
2B+2C=6/50.
But C=1/50.
On substitute c in above eqn we get as,
2B=4/50 and,
B=1/25,
Hence B=25 days.
Shree said:
8 years ago
Thank you for providing Clear and detailed explanation.
Imran said:
7 years ago
A+B=1/10. -----> (1)
A+B+C=(1/10 + 1/50) = 3/25.
A+A=3/25......(A = B+C).
A=3/50,
3/50 + B=1/10,
B=1/25,
B alone does it in 25 days.
A+B+C=(1/10 + 1/50) = 3/25.
A+A=3/25......(A = B+C).
A=3/50,
3/50 + B=1/10,
B=1/25,
B alone does it in 25 days.
Geeta vandana said:
7 years ago
@Awoke.
Your short cut method is nice. Thanks.
Your short cut method is nice. Thanks.
Logi said:
7 years ago
Thank you @Nagu.
Shivangini sharma said:
7 years ago
A = B+C.
A+B = 1/10.
Therefore
A = 1/10 - B.
1/10 - B = B + 1/50.
-B - B= 1/50 - 1/10,
= -2B = -4/50,
2B = 4/50,
100B = 4,
B = 4/100,
B = 1/25.
A+B = 1/10.
Therefore
A = 1/10 - B.
1/10 - B = B + 1/50.
-B - B= 1/50 - 1/10,
= -2B = -4/50,
2B = 4/50,
100B = 4,
B = 4/100,
B = 1/25.
Alekya said:
7 years ago
@Saurabh.
We get A's rate = 6/2 = 3 units/day.
Here, how it comes 6/2?
We get A's rate = 6/2 = 3 units/day.
Here, how it comes 6/2?
Baba syed said:
7 years ago
@Awoke.
Superb Explanation, Nice keep it up.
Superb Explanation, Nice keep it up.
Bhaskar said:
7 years ago
a=b+c.
a+b=10,
c=50.
then b+c+b=10.
2b+c=10,
2b=10-50,
2b=40,
b=20.
a+b=10,
c=50.
then b+c+b=10.
2b+c=10,
2b=10-50,
2b=40,
b=20.
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