A's one day's work =`1/10`
B's one day's work =`1/12`
C's one day's work =`1/15`
A, B and C's one day's work =`1/10+1/12+1/15`
`=(6+5+4)/60=15/60=1/4`
Let the work completed in x days
∴ A's 2 days work + B's (x − 3) days work + C's x days work = 1
`⇒2xx1/10+("x"-3)xx1/12+"x"xx1/15=1`
`⇒1/5+("x"-3)/12+"x"/15=1`
`(12+5"x"-15+4"x"=60)/60` ...(L.C.M of 5, 12, 15 = 60)
⇒ 9x = 60 − 12 + 15
⇒ 9x = 63
`⇒"x"=63/9=7`
∴ Work will last for 7 days
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Correct Answer:
Description for Correct answer:
Let the required days be x.
A works for (x - 2) days, while B works for x days.
According to the question,
\( \Large\frac{x - 2}{10} + \frac{x}{20} = 1 \)
2x- 4 + x = 20
3x = 24
x = 8 days
Part of solved Time and work questions and answers : >> Aptitude >> Time and work
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Similar Questions
The completion of the work would have been scheduled assuming that A & B will work together for completing the work.
Let us suppose it to be x days.
but,
B worked for x - 2 days.
Let the total work = L. C. M (10, 15)
= 30 units.
A completes → \(\dfrac{30}{10}=3\) units/day
B completes → \(\dfrac{30}{15}=2\) units /day
\(x=\left(\frac{10×15}{10+15}\right)=\frac{150}{25}=6 \) days
For 4 days, A & B worked together
Work done = 4 × 5 = 20 units.
Remaining work = 10 units.
We need to find how much time A will take to complete 10 units of work.
A completes 3 units in 1 day
A completes 10 units in 10/3 = 3.33 days.
Total days → \(4+3\frac{1}{3}=7\frac{1}{3}\) days
Alternate Method
Formula:
W = RT
Where W is work and T is time
Given, A complete a work in 10 days
A complete a work in 15 days
Let, 1 work = 30 unit (for simplification: LCM of 10, 15)
Person |
R |
T |
W |
A |
R = W/T = 3 |
10 |
30 |
B |
R = W/T = 2 |
15 |
30 |
If A & B together do a work then, R = R(A) + R(B) = 3 + 2 = 5 |
|||
A + B |
5 |
T = W/R = 6 |
30 |
Hence, both together can complete a work in 6 days.
If 'B' leaves 2 days before the scheduled completion of the work then A alone will do the work for the last 2 days.
Person |
R |
T |
W |
A + B |
5 |
4 |
W = RT = 20 |
Now remaining work is (30 – 20 = 10), which completed alone by A
Person |
R |
T |
W |
A |
3 |
T = W/R = 10/3 |
10 |
Now total time required to complete work by both if 'B' leaves 2 days before the scheduled completion
Time = \(4+\frac{10}{3}=7\frac{1}{3}\) days