Time And Work Notes 23-06_575592_crwill.pdf

Time and work

1. fe TIPE | PEN

X and Y can complete a work in 9 days and 36 days, respectively. X begins to do the
work and they work alternately one at a time for one day each. The whole work will
be complete in:/X aite Y war ard at amy: 9 far afte 36 fer Hye at wat HX art
aor YS area À site aa wes THU fet ard wea qu are Ft
fen à ye rm

males mia odas sha
5 E)
Ss y
Sd Bd
4
36 cru)

+ Cxety) —> aeyole of 2day = Sanit Work

(= +Yy)—> Feyete of
Zday x

= sx
14day = asunit

> 10gole of day = Luni
liday = 3sunit
A and B alone can do a piece of work in 4 and 9 days, respectively. In how many days
will the work be completed, if they both work on alternate days, starting with B?
A fre a wa amd ah wont: 4 sie 9 RN we wat Rae aH BA IS AT
ee art at are ft fe ge mt

CES DES @ 5 ws;
DL y
4d Sd (A+B) — 1 oycle of 2day = i3unit
36(1u)

2. (A+B) + 2 cycle of 2dqy > Hday

= 26unil
B= Iday = unit
AS Bday = Suit

sZdys = asunit

A, B and € can do a piece of work in 30 days, 40 days and 50 days, respectively.

Beginning with A, if A, Band C do the work alternatively then in how many days will
the work be finished 2/8, B afte C Ua wrt at mr: 30 fer, 40 für aft so fer HT
ar Gat br aie an at wo A À eit Ra A fer ar ae À,
it ad Fam fer qa rem

1 a
CES () 363

(36 (a) 3955

A 8 Ss
Y
a a (Aves) > 1cyole of
av ad = 0
6006ru)
SO, CA+BtC) > I2oyolexad = Urxız
day = 564 unit
+ A—> 1doy = 204nil

* B—1day = isunit

+ C— day = unit

38 fzday = Sooynil

Ravi can do a piece of work in 40 days and Sudha can do the same piece of work in 60

days. If they work on alternative days starting with Sudha on the first day, then in
how many days will the work be completed ?

3. fa fart a 40 fare Hae rer & afte Gar set o Far ar Wet a a
ca at ror gan À eh faite à er SET fer am wT €,

cam Far fe qe Em
(a) 40 (6) 60 (9 48 (a) 45
Bw s
tod gad +(R4s) > Loyole of — Su
XA 2d0y
120 ru)
So,

+ CRES) — 24 cycle x 2day = 24xs

48 day —> 120Uni+

Ans=48 day

Amar can complete a work in 15 days, and Prem in 12 days. Starting with Amar, they
‘work on alternate days. In how many days will the work be completed?
are uam ad 15e af A 12 Fe of ame ir mr wa ELA CHAT
foi Hani we fh ard fart mem

2 1 1
6) 132 () 22 lo 132 CES
A P
OL
isd 12d e anejo, = gunit

WA 2

tra

+ AP —> 6cyolex2d = 6x9
12 day = Su unit
1day = 4unit
Hay = 2unit
132 doy = Sounit

4. À and B takes 3 and 6 hours, respectively, to complete a certain work. if they work on |
the alternate hour. How long will it take them to accomplish the task?

ar Fra ad at gr AA ite BON HM: 3 ae 6 WE em ae a ic WE r
Tam amd # ar amd or a Ree we aT

(a) 3 hours (b) 4 hours (c) 2 hours (d) 4.5 hours
«By NZ
A+B) => 1 cycle of
sk sh (as) ee = Bunt
tru)
so

(+8) — 2oyele of
21s

ahs = sunt

Mhs= 2 has

A and B can complete a piece of workin 12 days and 18 days, respectively. If they work
at it alternatively. A begining, in how many days will the work be finished?

AA ofte rd at amt: 12 fet afte 18 fer aT art WHA ELA ON aA EE ATE
Aa 8 ani aed fat feat fe Ward ere et eM

CEA (o) 143 (0 153 (a) 152
Boy
124 18d (A+B) => A cyoleor _ $
KA da = sunit
361)

CA+8) — + cycle x 24 = 5x4
14 day = 3suniy

day = aunit

day

Séunit

5. 1.

Supraja and kausalya can complete a work in 30 days and 20 days, respectively. If supraja
starts the work and they work on alternate days, in how many days will 75% of the
work be completed2/Gurar sit area wa ann at want: 30 fet afte 20 fer qu at
wet Fu ara ae at ROM gro ote ees rar MHA fe a
ved ot 7596 aa Pad fer ge eo,

(a) 28 (6) 24 (0 20 (a) 18
2, y, «(s+1) > cor EE
4
(ru) "751 = 3 x60 = ysunit
* AHB= Sogolexad= sxg
18 day =ysumit
Ans = \eday

‘Two women, Ganga and Saraswati, working separately can mow affeldin hrs. and 22 hrs.
respectively. I they work in stretches of one hour alternatively, Ganga beginning at 9 am.
when will the mowing be fnished?/&t frend, xi ah erent, EE arm ar TT
an at aa me: 8 woe 12 OH ae à mt a EEE eS si
Sa at, sie gar 9 ak Ba ge att, dt Oe eT ar a TT?

(a) 6:30pm (b) 4:30pm (c) 8:30pm (d) 7:30pm
G, Ss
CU + Cars) aaa |
an
Bow

+ (G48) > y cycle of ames =
Shy

+ G—Lhs = sunit

+ S—othy = ait

xy
unit

hss = aut

6. 13. A can complete a piece of work in 25 days while B can complete the same work in 30
days. They work on alternate basis, starting with A. Both A and B follow this pattern for
5 days and then A leaves the work. In how many days will finish the remaining work?
A an wom a 25 Fe pe a a a B et a 30 fe HT BE vo A
À ge fer ab arar we wa aA ELA AR aA EE, A afte Br s Fer à fe qu
eh am at ate fire A are dB a A fer Wg at

2 3 2 |
(a) 245 (b) 55 (e) 24 (a) 55 |
Ay B Il
& |
| ri |
HA |
|
E) &
Sdayx6 2dayxs |
1euni 1ounit " 1So-28 |
mn |
Bon |

= 2
12 = 202 dy
14. R,SandTean finish a work in 20, 15 and 10 days, respectively. R works on al days and
5 and T work on alternate days with Y starting the work on the frst day. In how many
days is the work finished?/R, S off T Far wr wit zm: 20, 15 Sfr 10 Fei TT
Feat 1 R wit fer a eet ate 5 afte fs fet we wa FT
fet a age aoe a fr fet HT em $

> s7
CE CE 07 Lars
R, S, al RAT,
SN RAT, RS, = 2a
20d “igs od Su Ft = feng Tego ck
60
So. CRIT) #(RtS) > 3 cycle oF 2day = 16x3
6 day = ygunit
+ (RET) 1 day = gunit
+(R+S) edgy = aunt Ans 134 =52
| 5

| F3day = Gounit

7. A,B and € can do a piece of work in 11 days, 20 days and 55 days respectively. If B |
works daily and is supported by A and C on alternate days beginning with A, then in |
how many days will the work be finished?/A, B Sfr C war am mr: 11 fat, 20 fet ||
ai 55 er yon are a B wien ard art ae A aq am EE TT el |
BW swat À af C ame warm at me ere fewer EM?

(2) 10 CEE (©) 12 CE |
|
A
y $
u 20 ss
lt |

naa 1eycle of |
SN + Sun = Youn “ade
(N+8)(8+c) > uayolex 2day = usxu |
Bday = sey unit
ldy = aiunit
$day = sunit

|
|
9jday = 220unit |
|
||
|

8. 2

112 carpenters working 6 hours a day can make 460 chairs in 240 days, then number
of chairs made by 18 carpenters in 360 days each working 8 hours a day.

“af 12 ae 6 We WR am ar ao wil 240 fect Ham wank &, ot 18 aes, 9 UE
‘afer a ara 360 Pt Rett fiat arti?

(a) 1320 (b) 1380 (c) 1260 (d) 920

Mıxhixdı _ Maxhaxda

wr We
12x6x240 _ 18x8X360
760 Rz
We = Uioxg
Ll = 1360 +

16 labour do a work in 6 hour per day and make a wall of size 150 m long ,20 m width
and 12 m high in 25 days. Then find in how many days 12 labour do a work 8 hour per
day and make a wall of 800 m long, 15 m width and 6 m height.

16 wag 6 fr are 150 HA, era, 20 Mi. cist wa 12 oA, Bett tare 25
‘er ara ent tare fire 12 TE 8 WE wae ec TH 800 wh, ere, 15 MARA
an 6 i Set rare a ar feo fer ar ra A?

(a) 50 days (b) 30 days (6) 40 days (a) nor
Maxhaxda
Wa
16x6x25 _ 12x8xd2
50x20xR ” Booxisxt
Da = 2642
= Sodays

30 men working 8 hours per day can diga pond in 16 days. By working how many hours
per day can 32 men dig the same pond, in 20 days?/afafier 8 #2 wrt ack are 30 YoU
UH mera a 16 fei Hate weet G1 32 Gout at set wera at 20 RA fore
sais Re a er are eh?

(a) 6 hours/day — (b) 5 hours/day (c) 7 hours/day (d) 8 hours/day

9. Pix hrkdi Maxhaxdr
SR "un
> Boxexte _ a2xhx20

CR
H= éhsldgy

Shyam can complete a task in 12 days by working 10 hours a day. How many hours a
day should he work to complete the task in 8 days?/t far # 10 12 wre ae q, vara
Part ward at 12 eer a ane wera El fai a a fe sh a
2 ani af

(a) 14 (b) 16 CES (a) 15

Mıxhıxdı Maxhzxda

Kr Ta
SXIOXIZ _ Sxaxh

Ww mn

= Ishelday

1127 people, working 8 hours a day, can complete a task in 12 days, then in how many
days will 18 people finish the task, working 9 hours a day? /afe 27 itt ws fet à 8 We
arm ee 12 Pe ur aT ee wR E, 18 ie Re 9 Ea ec
a at fat fet HT aA?

(0) 18 days (b) 15 days (6) 16 days (a) 20 days

Mixhıxdı_ _ Maxhaxdz
hi Wa

29x8xI2

10. Some persons can do a piece of work in 12 days. Two times the number of such
persons will do hall of the work ina wate Fret ward a 12 fet à ra art WHR
€ A a amd ae at Psat feet A eet we Tat €?

(0) 9 days (b) 6 days (6) 5 days (a) 3 days

> zu _ axexd

ay

Dy=3

If men working p hours per day for p days produce p units of work, then the units of
work produced by n men working n hours a day forn days is:

fe P om Pe fe a P fa PP An a A
mn an PR fre a AR,

a E E = =
CE CE CE © À
PxPxp _ nxhxh
PT

pra nd

[7]

wen?

„=

Iftwo persons, with equal abilities, can do two jobs in two days then 100 persons with
equal abilities can do 100 similar jobs in fret are art ett 2 Ft à 2 ann aA
LE Ah, 100 rt er art win SER RE © 100 ara Pr Re Ha N?

(a) 100 days (b) 10 days (6) Sdays (8) 2 days

11. 10.

1.

12 monkeys can eat 12 bananas in 12 minutes. In how many minutes can 4 monkeys
eat 4 bananas?/12 at 12 U 12 Hard, a Part à à a?

(a) 4 minutes (b) 10 minutes (¢) 12 minutes. (4) 8 minutes
Mıxtı _ Maxta
y a
A
mA

t2= 12iminulos

A does half as much work as B in three-fourth of the time taken by B. If together they
take 18 days to complete the work, how much time shall B take to do it alone?

B ar Fer ea Sra, A a me fo 18 fet
ae er at Gat 8 FRR a aT FA wt?

(2) 30 days (6) 35 days (©) 40 days (4) 45 days
ARS _ Bxi
2 2
A-2
a3

TU = (A+8)x18d
= sxe
Sounit

= 20day
‘A does half as much work as Bin one sixth of the time. If together they take 10 days to
complete a work, how much time shall 8 take to do it alone?

BA ee A, B ai goer re am rc Br ae a eee 10 Ha ar
cd, at or a A fox am aM?

(a) 70 days (6) 30 days (©) 40 days (4) 50 days

12. = ==

TH =(A+8)x10d
4x10
Yo unit

"Then. Tw _ Mo

=
| = Hoday

12. A can complete $ work of B in = time than B, if they together complete the whole
work in 10 days then A alone can complete the work in how many days.
ara ma A
cam ah font Ar
(a) 213,19 (b) 253,20 (0) 40, 30 (a) 30, 40

Be
E

TH= (A+B)x10d
(3+10)x10
19x10

190 unit

13. 2.

14.

15.

Some carpenters promised to do a job in 9 days but 5 of them were absent and
remaining men did the job in 12 days. The original number of carpenters was.

ay agg Pat corm a 9 Rect HT wee ar aren eae Ahr SH Bs cir ara Tet
Laia au air fi re ar BE, ag a Wem we a?
(a) 24 (b) 20 (o) 16 (a) 18

A certain number of persons can complete a work in 34 days working 9h a day. Ifthe
number of persons is decreased by 40%. then how many hours a day should the
remaining persons work to complete the work in 52 days?

ay cafes aña 9 de ard are ada 34 fei à qu ae wet fh ale a at
A St 40% ae ar aaa, aaa fer A set ard at aT as fe
Tr fer feat oe ard wet wd?

(a) 9 (b) 10 (d 8 (d) 12

2
3

> 5x9x32 _ 3xsixh
wo We

H= lohrs

"X number of men can finish a piece of work in 30 days. there were 6 men more, the
work could be finished in 10 days less. The original number of men is.

X gent at deo Fort aaa wt 30 er H are want ale 6 qe site om ad eme 10
fer wed were Gt rie, a Rat a ee gra TE

(a) 6 (b) 10 (o) 12 CES

14. 16.

y ru,

| ar.

If the work done by (x 1) men in (x + 1) days and the work done by (x + 2) men in (1)
days are in the ratio 9:40, then the value of xis equal to:

aa (1) ft ara (n+1) RARA Pr wor (2) fi à a (A 1)
et fg a wr organ 9 10 À, m ara TT

(a) 5 (b) 6 (co) 7

(a) 8

Ger) _ re) 2 (eo (et) | Ge+a)be-1)
D + 7

To o

EN > lox+io= 908
5 D
==8

10%? 10 = 9x%+2-18

=?-sx+@=0

SR 8x-2048=0

(2-8) <1 (se-8)=0
(x-8) ae) =0

8. 2-2

A road of 5 km length will be constructed in 100 days. So 280 workers were employed.
But after 80 days it was found that only 32 km road was completed. Now how many
more people were need to finish the work in the specified time?

5 Re, wet ge 100 REA anh fet 200 wang a we era an APA 80
‘es arg ce fs se al Rest age a wf t,t am at era wT aS ft
‘at GA at ee eet at ee #7

(a) 480 (b) 80 (e) 200 (a) 100

15. 19.

Total Wosk = Skm
Time Pesios = 100 day
Woskes employed = 280

> 280x80d _ (280+) x20
ro te
> 480 = 280+>

x = 200 meh

‘Aman undertakes to do a certain work in 150 days. He employs 200 men. He finds
that only a quarter of the work is done in 50 days. The number of additional men that
should be appointed so that the whole work will be finished in time is:

um ante fered arm at 150 PA ye wea a Sa Sear À fe gaa Fer aE 200 Tint wT
‘am we ear a 50 eat a ag a Te À Pa et fem ae are, a AA AT
are Tr St a a eT whe?

(a) 75 (b) 100 @ 125 (a) 50

> Boomxsod | (100+2é)x1004
y 3
300 = 20042
& = 100men

35 persons are engaged to complete a work in 60 days. After 32 days it is observed

E
ke (fa ew a in er a

‘engaged to complete the remaining work in the said period is:
‘fart art a 60 Part Hq amet fore 35 wafer a era are 1 32 Fett are wa

aor a cr (E) af en ah gr rn ec a se ate Hg EE

& fon frat afte fit reg eh?
(a) 20 (b) as (o 30 (a) 25

16. > 35mas2d _ (ósto)xaed
HA

> 12x35 = 1x35+T7e

Sxas = 4x
ss = x
=-=25