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 3 of 15.
Shiva krishna kanaparthi said:
8 years ago
Total work = LCM of 10 and 50=50 units.
(A+B)'S 1 DAY WORK = 50/10= 5 UNITS PER DAY.
C'S 1 DAY WORK = 50/50= 1 UNIT PER DAY.
SINCE WE HAVE A=B+C AND A+B=5.
A-B=1----------(1)
A+B=5----------(2)
SOLVING ABOVE EQUATIONS WE GET B= 2 UNITS PER DAY.
SO NUMBER OF DAYS TO COMPLETE THE WORK FOR B= 50/2 = 25 DAYS.
(A+B)'S 1 DAY WORK = 50/10= 5 UNITS PER DAY.
C'S 1 DAY WORK = 50/50= 1 UNIT PER DAY.
SINCE WE HAVE A=B+C AND A+B=5.
A-B=1----------(1)
A+B=5----------(2)
SOLVING ABOVE EQUATIONS WE GET B= 2 UNITS PER DAY.
SO NUMBER OF DAYS TO COMPLETE THE WORK FOR B= 50/2 = 25 DAYS.
SALEEM BALOCH said:
9 years ago
A = B + C
A + B = 1/10
C = 1/50
SO,
A + B + C = 1/10 + 1/50
BECAUSE A = B + C
REPLACE THE VALUE OF A.
SO IT IS,
B + C + B + C = 1/10 + 1/50
2(B+C) = 6/50 OR 2(B + C) = 3/25
B + C = 3/25 * 1/2
B + C = 3/50.
(C=1/50) MINUS C ON BOTH SIDES
B + C - C = 3/50 - 1/50,
B = 2/50 OR 1/25.
25 DAYS FOR B.
A + B = 1/10
C = 1/50
SO,
A + B + C = 1/10 + 1/50
BECAUSE A = B + C
REPLACE THE VALUE OF A.
SO IT IS,
B + C + B + C = 1/10 + 1/50
2(B+C) = 6/50 OR 2(B + C) = 3/25
B + C = 3/25 * 1/2
B + C = 3/50.
(C=1/50) MINUS C ON BOTH SIDES
B + C - C = 3/50 - 1/50,
B = 2/50 OR 1/25.
25 DAYS FOR B.
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.
Shweta Rathi said:
7 years ago
Since we are given with the condition -
A=B+C ------1 (eqn).
C's 1-day work = 1/50.
(A+B)'s 1-day work = 1/10.
Therefore, using eqn 1.
A+B = 2B+C,
1/10 = 2B+ 1/50,
2B=40/500,
B=1/25.
B alone can finish work in 25 days.
Hope this method will help you understand this question easily.
A=B+C ------1 (eqn).
C's 1-day work = 1/50.
(A+B)'s 1-day work = 1/10.
Therefore, using eqn 1.
A+B = 2B+C,
1/10 = 2B+ 1/50,
2B=40/500,
B=1/25.
B alone can finish work in 25 days.
Hope this method will help you understand this question easily.
Palkin singla said:
1 decade ago
Let work done by A = X.
Same work is also done by B+C = X.
A = X.
B+C = X.
C=1/50 ---->[1].
A+B = 1/10 ---->[2].
Putvalue of a in 2nd eqn and C = X - B in 1st eqn.
We get two equation.
B+X = 1/10.
X-B = 1/50.
By solving we get B = 1/25.
Which is our requirement.
Have a nice day.
Same work is also done by B+C = X.
A = X.
B+C = X.
C=1/50 ---->[1].
A+B = 1/10 ---->[2].
Putvalue of a in 2nd eqn and C = X - B in 1st eqn.
We get two equation.
B+X = 1/10.
X-B = 1/50.
By solving we get B = 1/25.
Which is our requirement.
Have a nice day.
Shashidhar B Challamarada said:
4 years ago
This problem we can do it in a simple way.
(A+B)'s 1 day's work = 1/10;
C's 1 day's work = 1/50;
A's 1day's work = (B+C)'s 1day's work;
i.e. A+B = 1/10;
(B+C)+B = 1/10;
2B+C = 1/10;
2B = (1/10) - (1/50);
2B = 4/50;
B = 2/50;
B = 1/25;
So, B alone can do it in 25 days.
(A+B)'s 1 day's work = 1/10;
C's 1 day's work = 1/50;
A's 1day's work = (B+C)'s 1day's work;
i.e. A+B = 1/10;
(B+C)+B = 1/10;
2B+C = 1/10;
2B = (1/10) - (1/50);
2B = 4/50;
B = 2/50;
B = 1/25;
So, B alone can do it in 25 days.
(4)
Nagu said:
2 decades ago
Hi Guys,
In this problem
A's one day work is equal to (b+c)'s one day work
A = (B+C)
So a+b+c become 2A here they taken instead of b+c= a
so A+B+C = A+ (B+C) = A+A becasue B+C=A
3/25 = 2* (A's one day work)
so 2* A's one day work
I THINK YOU ALL UNDER STOOD THE TRICK..
In this problem
A's one day work is equal to (b+c)'s one day work
A = (B+C)
So a+b+c become 2A here they taken instead of b+c= a
so A+B+C = A+ (B+C) = A+A becasue B+C=A
3/25 = 2* (A's one day work)
so 2* A's one day work
I THINK YOU ALL UNDER STOOD THE TRICK..
(1)
Julius Openy said:
5 months ago
Given:
A = B + C.
A + B = 10,
C = 50.
Solution :
A + B = 10.
(A + B)'s one day way is 1/10.
A + B = 1/10 ---> 1
from A = B + C ---> 2
Substitute eqn 2 in 1;
B + C + B = 1/10,
2B + 1/50 = 1/10,
2B = 1/10 - 1/50,
2B = 4/50,
B = 1/25.
B alone can do the work in 25 days.
A = B + C.
A + B = 10,
C = 50.
Solution :
A + B = 10.
(A + B)'s one day way is 1/10.
A + B = 1/10 ---> 1
from A = B + C ---> 2
Substitute eqn 2 in 1;
B + C + B = 1/10,
2B + 1/50 = 1/10,
2B = 1/10 - 1/50,
2B = 4/50,
B = 1/25.
B alone can do the work in 25 days.
(18)
Varun said:
1 decade ago
First calculate the one day work of A+B+C = 1/10 + 1/50 = 3/25
Then given is A's work time = B+C's Work time...
So we can put "A = B+C" in (A + B + C = 3/25)
B+C+B+C = 3/25
2B+2C=3/25
Put C's one day work=1/50
2B+2*1/50=3/25
B=1/25
So B Time value=25 Day
Then given is A's work time = B+C's Work time...
So we can put "A = B+C" in (A + B + C = 3/25)
B+C+B+C = 3/25
2B+2C=3/25
Put C's one day work=1/50
2B+2*1/50=3/25
B=1/25
So B Time value=25 Day
Harsha said:
10 years ago
A -> B+C (given).
A+B -> 10.
C -> 50.
Taking L.C.M we get 50.
So A+B -> 10 (5) because 10*5 = 50.
C -> 50 (1) because 50*1 = 50.
A+B+C = 6.
As B+C can be replaced with A.
A+A = 6.
2A = 6.
A = 3.
Then B = 5-3 = 2.
So, 50/2 = 25 days answer.
A+B -> 10.
C -> 50.
Taking L.C.M we get 50.
So A+B -> 10 (5) because 10*5 = 50.
C -> 50 (1) because 50*1 = 50.
A+B+C = 6.
As B+C can be replaced with A.
A+A = 6.
2A = 6.
A = 3.
Then B = 5-3 = 2.
So, 50/2 = 25 days answer.
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