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 6 of 15.
Neil said:
1 decade ago
A=B+C.
A+B+C = 1/10+1/50=6/50.
(B+C)+B+C = 2B+2C=6/50.
B+C = 6/100.
B = 6/100-1/50 = 1/25.
Therefore, B = 25 days.
A+B+C = 1/10+1/50=6/50.
(B+C)+B+C = 2B+2C=6/50.
B+C = 6/100.
B = 6/100-1/50 = 1/25.
Therefore, B = 25 days.
Rohit said:
1 decade ago
I think its easy.
A = B+C ------ (i).
Then,
1 day work of A+B = 1/10.
1 day work of C = 1/50.
Now the Total Work of A+B+C = (1/10+1/50) = 3/25 .... (ii).
From eq (i) put A in place of B+C in eq (ii),
We get 2A = 3/25 = 3/50.
From eq (i),
We know value of A & C.
Put in eq (i),
3/25 = B + 1/50.
B = 1/25.
B= 25 DAYS.
A = B+C ------ (i).
Then,
1 day work of A+B = 1/10.
1 day work of C = 1/50.
Now the Total Work of A+B+C = (1/10+1/50) = 3/25 .... (ii).
From eq (i) put A in place of B+C in eq (ii),
We get 2A = 3/25 = 3/50.
From eq (i),
We know value of A & C.
Put in eq (i),
3/25 = B + 1/50.
B = 1/25.
B= 25 DAYS.
Sumasree said:
1 decade ago
@Rohit nice your answer, but we always follow shortcuts for speed up.
Ram said:
1 decade ago
Number of days taken by B and C to complete a work. with same number of days A alone can do it.
if C can do a work in 50 days. If B joins with C then it becomes 50 days/2 = 25 days for B and C.
A no.of days for work = B&C no.of days for work.
25 days = 25 days.
if C can do a work in 50 days. If B joins with C then it becomes 50 days/2 = 25 days for B and C.
A no.of days for work = B&C no.of days for work.
25 days = 25 days.
VRAJ said:
1 decade ago
A = B+C.
A+B = 10.
C = 50.
A+B+C = 1/10+1/50.
A+A = 1/10+1/50.
2A = 6/50.
A = 3/50.
A = B+C.
3/50 = B+1/50.
B = 3/50-1/50.
B = 2/50.
B = 1/25.
B CAN DONE THE WORK IN 25 DAYS.
A+B = 10.
C = 50.
A+B+C = 1/10+1/50.
A+A = 1/10+1/50.
2A = 6/50.
A = 3/50.
A = B+C.
3/50 = B+1/50.
B = 3/50-1/50.
B = 2/50.
B = 1/25.
B CAN DONE THE WORK IN 25 DAYS.
Anandhan said:
1 decade ago
a = a+b;
a+b = 1/10; together;-----------(1).
c = 1/50;
Take 1st equation,
a+b=1/10;
we know a = b+c; so substitute,
b+c+b=1/10;
2b+1/50=1/10;
2b=1/10-1/50;
2b=4/50;
b=4/100;
b=2/50;
b=25;
Thats it.
a+b = 1/10; together;-----------(1).
c = 1/50;
Take 1st equation,
a+b=1/10;
we know a = b+c; so substitute,
b+c+b=1/10;
2b+1/50=1/10;
2b=1/10-1/50;
2b=4/50;
b=4/100;
b=2/50;
b=25;
Thats it.
Suresh said:
1 decade ago
a+b = 1/10.
a = b+c eq.1.
c = 1/50.
Then a-b = 1/50 eq.2.
Solving 1 and 2 we get b = 1/25.
a = b+c eq.1.
c = 1/50.
Then a-b = 1/50 eq.2.
Solving 1 and 2 we get b = 1/25.
Serina said:
1 decade ago
How did you get 3/25, if you add 1/10 + 1/50 please explain in brief?
Sa_1 said:
1 decade ago
@Serina.
Its just LCM nothing else. Simple method.
A + B + C = 3/25.
Now A and B + C together time are same.
A = B + C.
A + B + C = 3/25.
B + C = 3/25 - A.
So we can write
A = 3/25 - A.
2A = 3/25.
A = 3/50.
Its just LCM nothing else. Simple method.
A + B + C = 3/25.
Now A and B + C together time are same.
A = B + C.
A + B + C = 3/25.
B + C = 3/25 - A.
So we can write
A = 3/25 - A.
2A = 3/25.
A = 3/50.
Shanu Verma said:
1 decade ago
A = B+C-----(1).
A+B = 1/10------(2).
C = 1/50-----(3).
B+B+C = 1/10 (put value of A from equation 1 in equation 2).
2B+C = 1/10 (as C = 1/50).
2B = 1/10-1/50 = 4/50 = 2/25.
B = 2/50 = 1/25.
B alone could do the work in 25 Days.
A+B = 1/10------(2).
C = 1/50-----(3).
B+B+C = 1/10 (put value of A from equation 1 in equation 2).
2B+C = 1/10 (as C = 1/50).
2B = 1/10-1/50 = 4/50 = 2/25.
B = 2/50 = 1/25.
B alone could do the work in 25 Days.
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