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Time and Work

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by

EMPERIND

on 8 October 2018

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Transcript of Time and Work

Ex 1:
15 men
can type
3240 pages
in
6 days
working
2 hours per
a day. how many men would be required to type
5400 pages
working
4 hours
per day for
3 days?
Sol:
P1 = 15
W1 = 3240
H = 2
D = 6
P2 = ? (x)
W2 = 5400
H = 2
D = 3
* Work is given .:. Then use formula 1
Ex II :
If 72 men can build a wall of
280 m length
, in
21 days
how many men could take
18 days
to build similar type of wall of length
100 m?

Sol:
P1 = 72
D1 = 21

W1 = 280

P2 = ? (x)
D2 = 18

W2 = 100

* Work is given then use formula 1
(iii)
39 persons
can repair a road in
12 days
working
5 hours
a day. in how many days will
30 persons
working
6 hours
a day complete the work.
Sol:
P1 = 39
D1 = 12

H1 = 5hours
P2 = 30

D2 = ? (x)

H2 = 6 hours
* work is not given, then use formula - 2
P1
H1
D1 =
P2

H2
D2
39 x 5 x 12 = 30 x
X
x 6
x = 13
(iv)
15 labours
complete a work in
10 days
working
6 hours
per day, if
18 labours
employed on that work and the work is to be completed in
5 days
then how many hours per day should the work be continued
Sol:
P1 = 15
;
D1 = 10

H1 = 6
P2 = 18
;
D2 = 5

H2 = ? (X)
* Working not given, then use formula 2
.:. P1 H1 D1 = P2 H2 D2
15 x 6 x 10
= 18 x X x 5

.:. x = 10
Type II
Based on efficiency
1. A is two times efficient then B =>
A B
5 Days 10 days
x
2x
x2
(ii) A is trice times efficient than B
=> A B
10 days 30 days
x
3x
(ii) A is four times efficient than B
=> A B
10 days 40 days
x
4 x X
4.

A is 50%
"more efficient" then
B
A
B
100%
150%
A
B
5.
A takes 50%
"more time"
than B
x
+
50% of x
For more complex problems
Ex:-
"A"
is twice as good
"B"
and
"B"

is twice as good as
"C"
if A and B can together finish a piece of work in
4 days
The
"C"
can do it by himself in:
Sol:
A B C
x days 2x 4x
* A + B completes a task in 4 days
.:. 1 day work => A + B
=
(ii)
A and B
together can do a work in
12 days.
B and C together do it in
15 days
. If A's efficiency is twice that of C,
Then The required for B alone to finish the work is.
let us take 1 day of work
B alone to finish the work alone is
.:. Substitute x value in Equation (i)
.:. B takes 20 Days
(iii) asha and Babu can do a job together in
7 days
Asha is 1 times as efficient as babu. Same job can be done by asha alone in?
let us take 1 day work
(iv) A can do a piece of work in
70 days
and B is
40% more efficient
than A. Then the number of days taken by B to do the same work is.
Sol :
A
B
70 days x days
140% 100 %
* B is more 40% Efficient Than
"A"
.:. B A

100% 140%
140% = 70 days
100% = x
.:. Remove (or) cancel percentages and cross multiply
140 x = 70 x 100
x = 50 days
(v) To complete a work.
A takes 50%
more time than B. if together they take
18 days
to complete work,
how much time shall B take to do it?
Sol:
A
B
x
+
50 of x
x
Type- III : Fraction of Work:-
Ex-(i) A can complete of a work in 4 days and B can complete of the work in 6 days.
in how many days can both A and B together complete the work?
Sol:
Ex (ii):
A can do of a piece of work in
5 days,
B can do of the same work in
9 days
and C can do of that work in 8 days. in how many day can all of them together do the work?
Sol:
(iii)
Sol:
(iii) A does work of a piece of work in
20 days
he calls B and they finish the remaining work in
3 days
how long B alone will take to do the whole work?
Sol:
(iv) A does
1/10 part of work
in
15 days
after that he completes the remaining work in
4 days
with the help of B
in how many days will A and B. Together do the same work?
Sol:
(v) A complete
2/3
of his work in
10 days.
Time he will take to complete
3/5
of the same work is .
Sol:
Step 1:
One day work done
Step 2:
Find Ratio
Step 3:
Find Share
1)
A can do work in
3 days.
B can do the same work in
2 days.
Both of them finish the work together and get
Rs.150

what is the share of A?
Sol:
2)
A and B under took to do a piece of work for
Rs. 4500
Alone could do it in
8 days
and B alone in
12 days
With the assistance of C they finished the work in
4 days
then C's share of money is:
Sol:
3. Three persons undertake to complete a piece of work for
1200 Rs.
the first person can complete the work in
8 days
second person in
12 days.
and third person in
16 days
They complete the work with the help of a fourth person in
3 days.
What does the fourth person get?
Sol:
4.

A, B, C
completed work costing
Rs.1800
A worked for
6 days
, B for
4 days
and C for
9 days,
If their daily wages are in the ratio of
5 : 6 : 4
, how much amount will be received by A?
Sol:
Daily wages
=>
5 : 6 : 4
6 x 4
4 x 6
9 x 4
A : B : C = 5 : 4 : 6
120
5.
a man and a boy received
Rs.800
as wages for
5 days
for the work they did together. The man's efficiency in the work was three times that of the boy.
what are the daily wages of the boy?
Sol:
M + B = 5 days = 800
the man efficiency
is trice than the Boy
In term of days
in term of work
x : 3x
5 : 15
3 : 1
M : B
x3
6.
If
5 Men
(or)
7 women
can Earn
Rs.5250
Per day. How would
7 men
and
13 women
Earn per day?
Sol:
5 men = 5250
1 men = 1050
7 men = 1050 x 7
= 7350
1 men =
7 women = 5250
1 women =
1 women = 750
13 women = 750 x 13
= 9750
17 , 100
7
.
2 men
and
1 women
together can complete a piece of work in
14 days,
while
4 women
and
2 men
together can do it in
8 days.
If a man gets
Rs.600
per day, how much should a woman get per day?
Sol:
SHORT CUT
8.

A, B, C
together Earn
Rs.150
per day while A and C together Earn Rs.94 and B & C together Earn Rs.76 The daily Earning of 'C' is ?
Sol:
1.
A and B
together can complete a work in
3 days
they started but after
2 days
B left the work. If the work is completed after
2 more
days.
B
alone could do the work in how many days?
sol:
Normal Method:
2.
Ajay can do a piece of work in
25 days
and sanjay can finish it in
20 days.
They work together for
5 days
and then ajay goes away. In how many days will sanjay finish the remaining work?
Sol:
Short cut :2
3.
A and B
can do a piece of work in
60 days
and
75 days
respectively. Both begin together but after a certain time
A
leaves off. In such case,
B
finishes the remaining work in
30 days.
After how many days did A leave?
short cut :1
Normal method
Short cut : 2
4.
A
can complete a piece of work in
40 days
. He starts working, but having some other engagement leaves after
5 days.
Thereafter,
B
completes this work in
21 days.

How many days would A and B take to complete this work working together?
Sol:
Normal method
Short cut I:
short cut: II
1.
Ajay and sunil together can complete a piece of work in
10 days.
sunil and sanjay in
15 days
and sanjay and Ajay in
20 days,
They worked together for
6 days,
and then ajay leaves. Sunil and sanjay worked together for
4 more days
and sunil leaves.
How long will sanjay take to complete the work?
Sol:
2.
A, B and C can do piece of work in
16, 32 and 48
days respectively. They all begin together. A work continuously till it is finished,
C leaves
the work
2 days
before its completion. and B leaves the work the work 1 day before its completion,
In what time is the work finished?
Sol:
3.
A and B
can finish a job in
10 days,
while
B and C
can do it in
18 days.

A
started the job and worked for
5 days
and left the job . Then
B
worked for
10 days
and remaining job is finished by
C
in
15 days.

In how many days
C
alone have finished whole job?
Sol:
x
.:.
.:.
=
4
2
1
15
10 days
8
=>
(A +B) x
39
120
3
10
4.
A can complete a piece of work in
40 days
.
He starts working, but having some other engagement leaves after 5 days. Thereafter
B

completes this work in
21 days
.
How many days would A and B take to complete this work working together?
sol:
Normal Method
Ex 1:
15 men
can type
3240 pages
in
6 days
working
2 hours per
a day. how many men would be required to type
5400 pages
working
4 hours
per day for
3 days?
Ex II :
If 72 men can build a wall of
280 m length
, in
21 days
how many men could take
18 days
to build similar type of wall of length
100 m?
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