Question

x,y and z can do a piece of work in 10,15 and 30 days respectively. thet started work together, but y left after 2 days. in what time will the remaining work be completed by x and z​

Answer 1

Solutions :-

Given :
x, y and z can do a piece of work in 10, 15 and 30 days respectively.

x's one day work = 1/10
y's one day work = 1/15
z's one day work = 1/30

(x + y + z)'s one day work = 1/10 + 1/15 + 1/30
= (3 + 2 + 1)/30
= 6/30 = 1/5

(x + y + z)'s two days work = 1/5 × 2 = 2/5


Remaining work = 1 - 2/5
= (5 - 2)/5
= 3/5


(x + z)'s one day work = 1/10 + 1/30
= (3 + 1)/30
= 4/30 = 2/15


Find the time taken by x and z to complete the remaining work :-

= Remaining work / (x + z)'s one day work
= (3/5) / (2/15)
= (3×15) / (2×5)
= 45/10
= 4.5


Hence,
x and z can complete the remaining work in 4 days and 12 hours.

Answer 2

X can do Work in=10 days
X's 1 day work=1/10

Y can do Work in=15 days
Y's 1 day work=1/15

Z can do Work in =30 days
Z's 1 day work in =1/30

(X+Y+Z) 1 day Work
=1/10+1/15+1/30
=3+2+1/30. (LCM=30)
=6/30

(X+Y+Z) 2 day Work
=6/30×2
=2/5

Let Total Work be=1
Remain Work=1-2/5
=3/5

X and Z Together 1 day work
1/10+1/30
=3+1/30
=4/30
=2/15

Days they take to complete work =15/2 days

Now Remaining work=3/5
(X+Z) 1 day work=2/15

Total days=Remain Work/(x+z) 1 day Work
Total Days=3/5÷2/15
=3/5×15/2
=9/2 days=4 1/2
Or 4 days 12 hours
As 1/2 of 24 hours=12

$\boxed{\mathbf{(X+Z)\: can\: do \:Remain \:Work\: in=4 \frac{1}{2}days}}$