Aptitude - Time and Work - Discussion
Discussion Forum : Time and Work - General Questions (Q.No. 9)
9.
A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
23 days
37 days
37
40 days
Answer: Option
Explanation:
| Whole work is done by A in |  |
20 x | 5 |  |
= 25 days. |
| 4 |
| Now, | |
1 - | 4 | |
i.e., | 1 | work is done by A and B in 3 days. |
| 5 | 5 |
Whole work will be done by A and B in (3 x 5) = 15 days.
| A's 1 day's work = | 1 | , (A + B)'s 1 day's work = | 1 | . |
| 25 | 15 |
 B's 1 day's work = |
|
1 | - | 1 | |
= | 4 | = | 2 | . |
| 15 | 25 | 150 | 75 |
| So, B alone would do the work in | 75 | = 37 | 1 | days. |
| 2 | 2 |
Discussion:
164 comments Page 17 of 17.
Joel said:
4 years ago
Whole work done by A is?
In 20 days 80%
In how many days 100%
80% in 20 days.
100% in x days ---- cross multiply.
100 * 20/80 = 25 days.
A completes work in 25 days.
Now A+B
20% in 3 days
100% in x days ---- cross multiply.
100 * 3/20= 15 days.
A+B complete work in 15 days.
now A's one-day work = 1/25.
A+B one day's work = 1/15.
now we want B,
B=(A+B)-A,
=(1/15)-(1/25)=>2/75............................B's one day's work,
Work done by B is (reciprocal of B's one day work) 75/2 days
now divide 75/2.
75/2=37 and the remainder is 1.
hence answer is 37*(1/2)days.
In 20 days 80%
In how many days 100%
80% in 20 days.
100% in x days ---- cross multiply.
100 * 20/80 = 25 days.
A completes work in 25 days.
Now A+B
20% in 3 days
100% in x days ---- cross multiply.
100 * 3/20= 15 days.
A+B complete work in 15 days.
now A's one-day work = 1/25.
A+B one day's work = 1/15.
now we want B,
B=(A+B)-A,
=(1/15)-(1/25)=>2/75............................B's one day's work,
Work done by B is (reciprocal of B's one day work) 75/2 days
now divide 75/2.
75/2=37 and the remainder is 1.
hence answer is 37*(1/2)days.
Milan said:
4 years ago
Here;
20 is 80 %,
25 is 100%,
A+B = 3 days this is 20 %.
20% * 5 = 3 * 5 for 100% work,
B= A+B- A.
B=1/15- 1/25,
B = 2/ 75 = 37.5.
20 is 80 %,
25 is 100%,
A+B = 3 days this is 20 %.
20% * 5 = 3 * 5 for 100% work,
B= A+B- A.
B=1/15- 1/25,
B = 2/ 75 = 37.5.
Suman said:
4 years ago
Hey Guys! Let's view this differently,
|80% = 80/100 = 4/5|
|20% = 20/100 = 1/5|
As/Q,
4/5 A = 20 => A = 25 --> 3 <-- Efficiency of A {as, TW/25=3}
LCM (25, 15) = 75 <-- Total Work, TW(say).
1/5 (A+B) = 3 => (A+B) = 15 --> 5 <-- Efficiency of A+B {as, TW/5=5}.
Since the Efficiency of A is 3 and A+B is 5, this implies, the efficiency of B is 2.
Now,
TW=75 and B's efficiency is 2,
So, no. of days needed by B is, 75/2 = 35.5 <--answer.
|80% = 80/100 = 4/5|
|20% = 20/100 = 1/5|
As/Q,
4/5 A = 20 => A = 25 --> 3 <-- Efficiency of A {as, TW/25=3}
LCM (25, 15) = 75 <-- Total Work, TW(say).
1/5 (A+B) = 3 => (A+B) = 15 --> 5 <-- Efficiency of A+B {as, TW/5=5}.
Since the Efficiency of A is 3 and A+B is 5, this implies, the efficiency of B is 2.
Now,
TW=75 and B's efficiency is 2,
So, no. of days needed by B is, 75/2 = 35.5 <--answer.
Anitha said:
3 years ago
Your explanation is short and good.
Thanks @Ajith.
Thanks @Ajith.
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