part mpred In Ihous =

(1)

28

Wednesday NOVEMBER 2007

332-33/Week 48

ARITH METIC FOR ALL

PiPes and Cistehns

FOmulas

1) T a pipe can i l t a känk in z hours

hon part fMed in houa & t a n k

) 24 a pipa can enplh a full tank in yhous

part mpred In Ihous

⁼

tank.

* * * * * * * * * *** ******

3)

^a

pipe tan fil a tänk In h o n s and

**************

fll ank inyha

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * - * * * * * * * * * *

anoer Ppe Can emplyte ( l a ) thn

Pipes, tte h e t Pant Aled tn hons

where o p in both the

A) P

^a

pipe Can l l a tank n h o n x and

f k kank In hons

a m o l

anothes Ppe Cam 2ply t u

h e u

(x >y), then

^Dn

openi ng both the

het pant emptied in hour Pip, th

DECEMBER 2007 W S W T F S

8 49

10 ₁₁ 12 13 14 15

5 ⁶ 17 I8 19 20 21 2

s 4 25 26 2 28 9

(2)

Thursdayy

13

Two pi pes AcmedB Cam 4:l a tank in 20 omd DECEMBER 2007

347-18/ Week 50

B

30 mintes respech vely2f koth bh Pipes aAe

take

Lu&ed oqette bhen how long wil it tak ts

H tank ?

20 minuis

Pipe4 alone Can f l Ea tank

Pipe Balou Can L: tu Tank n 30 m/n

2n e Min A A le

***************************************************************************************

* * * * * * * * * * * * * * * * * * * * * *

***********************************************************************************n*************************snossao*****sssasno***sn**

* * *******************************************

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

T. o w minutz A zB kogehur 4 + art A.h

**************************************************************.

3 + 2

******************** m************************************.************** *

bo

Paxt A tank

2

Thern fore A andB b gohar 4 ha Tank in 2 rins

Notes

ECEMBER 2007

MTW TFS

4 5 6 7 8

0 11 12 13 14 15 7 18 19 20 21 22 4 25 26 27 28 29

(3)

14

A Cis tenn tam be dby atap n 4 hou

Friday

DECEMBER 2007

348-17/Week 50

n

wula iE Com be enmptied by anobwr lap in 9hous.

Plooth bhe tap

a

Open ed imu tano w

Bhen aptir how muth Lime will Hhe Cstesn get 4lad ?

po

h e w tha Cistern 4:lled by fapA is paot

Ln

In l hour tu Cis tem emphad by tap B ispt

Here )

******************************nn*r*****************

12

********************************r*1*******n*******a**** *ene

***************

********************** ********

' L n Ihour b o th lap A and B

^{a u}

Opan

***********************************"********************* h h e t Part

* * * * * * ***************er************ *******a****** ************sser*****endses*****************see******************************re*************

- 4

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

********************************************************************************************************************************************************************************************* ******

36

*****h**************aah*rarass******** ***********a************** *************************************************************************************** ***w********Tn**

****n**asp******************************

7.2

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * t * * * * * * * * * * * * * * * * ****** * a * * * * *

Theraore boh kaps ARB am ope

Hhovn wilbe. Aled in i'n 7.2 hou

(DR)

net Pat Med

⁼

36

n bo mins

2n I min we

^net

fPsrn a 36x6o S 3612 3 2

JANUARY 200%

Notes

wk S MI WT F

Thuba be f ud in 432 mins

or) 7hows 12 minut

4 2 6 7 8 9 10 T1 12

1 4 16 17 I8 19 4 2 0 21 22 23 24 25 26

2 7 2 9 ) 1

(4)

Tuesday

18

352-13 / Week 51

DECEMBER 2007

3) Pipe A Cam Cam 4: H tol in 5hon piRBi,

h o n s m d pi pe C 'n 30 h o n . 2 au tta pipes a

Aan

opon in how many how wiu Bu

PAt nk f kd y A

ⁿ

1 hour

pot 9 om fiad by 8 n ho

Pont o tomk d 1 honr

30

honr

Pne Tomk lhd by A,,c

^{i n}

bt3+ o

30 30

3

T A B,am opomanwill Aod? 3hou.

Notes

D E E M I R 2607 M T W I F S

2 4 5 7 8

1 ) ! ^{12 13}^I4

1 9 29 2 1 22

9 ^{74 5} 2 ²⁷ ² ⁷⁹ⁱ

(5)

19

Wednesday

DECEMBER 2007

353-12/Week 51

4) Pipes A md B Com B Com l a tank in 5 md 6 honm

Ppe CCam emply it m 1 2 h o u . 24 all

tank

yu pech vely

****

thsee p e s opened ogather

^{r a n}

Ba t nk

l a d in hons

******************************* ****** **********r**** **

** *****.******************************************************** ****************************

Part l e d n h o n y Aomd B anc o e n

********************* .*** care**********************an.esee******************************************** *******************************************ranasra**.***. -*..**

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * i * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * i * * * * * * * * * * * * * * - * * * * *

30

*********************** **************...******.vaass**sses***.*.**...*.**.****.*.***********.*************..***********************..**.**********.os.-***.o*.ce. **

30

Pant emphi houY

* * *.**** **.t*************.*****i***remepn****

2

********************************** **** ****

n lhon

^{* * *} **********************************************************************************************

Na+ Part led h o n

^{* * *}

A4 B C

^m

open 3 0 1 2

* * **** ****************************************************************** ****************************************

2 2 - 5

17

60

tan will

^Le

krlled in o hours

A,B,u p e n

b

bo hon 3 hous

Notes

JANUARY 2008 Wk S M I W F

7x 3 5

6 7 8 9 1 0 1 1 2

1314 15 6 17 18 19 20 21 22 23 24 25 26 5 27 28 29 0 31

(6)

Quantitati k

372 Sol.

Then, second

pipe will

^fill ^{it in}^(x ¹⁰⁾

hours

x+10+ *

12

L e t the reservoir be filled

by

^first

pipe

^{in x} h o u r s .

r ( r + 10)

( x - 2 0 )

(x

⁺ ⁶⁾^a ⁰

(x+10) 12 x 14x -120 0

neglecting the-

^ve

value

_.

X = 20.

Ex. 4. A cistern has two taps which fill it in 12

minutes and

¹⁶

minutes

^{r e .}

emply pened, the

mpty the f

So,

the second pipe

^{will take} ⁽²⁰ 10) hrs i.e, ^{30 hrs}to

fill

the

res

ertively

There

^{is also}^a ^waste

pipe in

^the^cistern. ^When^{all the}three are oper

cistern

^is^fullin 20 minutes. How

long

^{will the}^waste

pipe

^{take to}

emat

th th

cistern?

Sol.

Work done

by

the waste

pipe

^{in 1}^minute

-ve sign means emptying

Waste

pipe

^willempty the full cistern in 10 minutes.

Ex. 5. An electrie pump can fill a tank in 3 hours. Because of a leak in the a it took 3hours to fill the tank. If the tank is full, how much time will the lenk ui

to empty it ?

Sol. Work done by the leak in 1 hour

The leak will empty the tank in 21 hours.

Ex. 6.

Two pipes

^can

fill

^a

cistern in 14 hours and

¹⁶

hours respectively. The pi

are opened simultaneously and it is found that due to leakago in the bottom it

32 minutes ^moreto fill the cistern. When the

cistern

is

full,

in what time will

the

empty it ?

Work done by the two pipes

ⁱⁿ

I

^hour

14 16 112

15

Sol

Time taken by these pipes to fill the tank = 112

hrs= 7 hrs 28

min.

Due to

leakage,

^time

taken

⁼ 7 hrs ₂₈

min

⁺ 32 15

min

8 hrs

Work

done

by

^(two

pipes

⁺

leak)

in 1

hour

⁼

8

Work done by

the leak in ₁

hour

12

112 112

Leak will empty the

^full

eistern

in 112

hours.

pipe

^C ^can

empty

^the

tank

^{in 30}

min. First A and

^B_are

opened. After

r e s p e c t i v e l y ,

7

A

w

Ex.

^{7. Two}

pipes

^A

and

^B^can

fill

a

tank in 36 min. and 46 min. rospect te

also opened.

In how much ime, the

tank

is

full

2 Sol. Part filled in 7 min. = 7 7

20 1 - 13

20

Remaining part

^-

(7)

s a n d C i s t e r n s

373

Net part fille a r t

filled

ⁱⁿ1 min. when

A,

^Band C are

opened 36'45 30 60

Now

A0

^{p a r t}^{i s}^filledⁱⁿ¹¹

13 Dart ^is

filled

ⁱⁿ

| 60 x

^{39 min.}

20

wo Dipes A and ^B ^can^fill^a tank in 24 min. and 32 min.

respectively.

^{If both}

S. e 0pened simultaneously,

after how much time B should be closed ^sothat

Total ^timetaken to fill he tank ⁼

(39

⁺ 7) min. ⁼ 46 min.

y

i

^{i s}

full in

¹⁸

minutes

^t

L e t

^Bbe closed ^after

x minutes. Then,

nart

filled by

^(A⁺ ^B)ⁱⁿ^x ^min.⁺

part

^filled

by

^A^{in (18}

- x)

^min.⁼ ¹

42+18- )x

1

1 7x 18E =1|

24

Tx+4 (18 ^- xd ⁼ 96 ^{X = 8.}

Hence, B ^must

be

^closed^{after 8} ^minutes.

EXERCISE 16A

(OBJECTIVE TYPE QUESTIONS)

Directions

Mark ( against

^the^correct

a n s w e r :

Two

pipes

^{A and}^B^{c a n}^fill^a ^{tank in}

20 and ³⁰^minutesrespectively.

If both

^the^pipes

are used together, then how

long

^{will it}^{take to}^{fill the}

tank ?

a) 12 min

(M.A.T. 2003)

(b) 15 min (c) 25 min (d) 50 min

A CIstern

^{c a n}^be^filled

by

^a ^tap

in 4 hours while it ^{c a n}be emptied

by

^another^tapⁱⁿ

hours.

If both the taps ^{a r e}

opened

s i m u l t a n e o u s l y , then after how much time will (Hotel Management, 1997)

the cistern

get filled1?

a) 4.5 hrs (b) 5 hrs

()6.5 hrs

(d) 7.2 hrs

A

^lap^can^fill^a ^tank^{in 6}hours. After half the ^tankis filled, ^three^{m o r e}^similartaps

E

^Opened.

What

is the total time taken to fill ^{the tank}completely ? a) 3 hrs 15 min

(c) 4 hrs (d) ^{4 hrs}^{15 min}

(b) 3 hrs 45 ^min (8.S.C. 2003)

aer

^tank^is^two-fifth

full. Pipe ^A ^{c a n}^fill

a tank in ¹⁰m i n u t e s and pipe ^B ^{c a n}

empty

(Bank P0. 1999)

l n

⁶ m i n u t e s . If ^{both the}pipes ^{a r e}^open,

h o w long ^willit take to e m p t y o r

l l the tank completely ? (c) ⁹^{min. to}^empty

a) 6

min.

to

empty

(b) ⁶ ^{m i n .}^{to fill}

d)

9

min.

to

fill 5. Pipe A

^can

fill

^a

(e) ^{N o n e}of ^these

t a n k in 5 h o u r s , pipe B ⁱⁿ¹⁰

h o u r s and pipe

pen, in ^how^{m a n y}

h o u r s will the

t a n k be ^filled?

pe C in 30 hours. If all (C.B.I. 1997)

Lhe pipes are open, .

(d) 3.5 (c) 3

a)

2

^{h a n d}^B

c a n fill ^a ^{t a n k}in ^{5 and}⁶

h o u r s

r e s p e c t i v e l y Pipe ^C

a l l the three pipes ^{a r e}

opened

t o g e t h e r ,

t h e n the ^tank

2 ^{(b) 2.5}

will be filled

12 hours.

^{(c) 3} ⁹ ^hours ^{(d) 4} ^hours

(a) 1 hours

( b ) 2 8 h o u r s (Bank P0. 2002)

17

(8)

c l A S S M A T e clASSMAte

Date Date

Page

ime and clig tante duPpo s

^a ^marn

Coves

^a

Les kan.

astonce at km/ur and

^an

egnal

tormula e

Speed istance2

dis tonca ak kro/hr, Ben tha avexage

ttme

Conyer Sion

Speed duiug the uohola,journ y i 4

k m looo

Ihour

^{6 o}^mnins

3600 Secs K

2 Im = 2 k m

roblenms

s e c = houv

3600

X 2h0O Sec How many minutes doesAdttya

hy

z r m/sec ako to Cover

^a

dis tante o 40o m

3600 Y ihe

^{u n s}

a t

^a

bpecd 3 20 km/ar

Specd diskan time

Ans:

5

3. 1 bhe ratio o the Speeds 9A and B s

Db AdityaSpead-2ob

Hexe

Y

ab,Ehen raho time Kakon t Cover

the Same d'c tanta s

(9)

alassMAte

Date

s tamtk

_age

T50 m

A Cyclist Coves a dis tant

in_ 2min 3o S e C. LLhat is e Speed ln km/hxof tteCyetist

change 9pecd to m/sec

369p Aws istaxmca 1 5 0 m

200 sec ti me 2min3oSec

36

(2x60)+30 Se

50 /sec

150 Secs

Specd distan

tme Specd = d'st,

Eime T5 sec

15

9 Eime

366 k

ime p00x Sec 5 x todo

1 8 km/hr

72 9e cs

min bo se c 3.A deg fakes 4 leaps fovevey5 leaps

sec min

of a hase but 3leaps oLadog Ore ena

60

72 Secs 72 x min f o 4 leaps o_ te hare. Compare ther

l . 2 minus Speds.

(10)

classmate

Date

Soln Oistante Covere d

_in

leap)=

dog

Page

him Was f the

m

Ymaintng _distanLe.

m e t e s

h a t

was

hie

Speed in Per Se Cond

Drstante Corered n hare

¹

leap . 1.Jm d*»

9lution

To tindSpecd ormula i s

32 48 Speed time

ime kaken h r 40 min

Specd rah'o dog: hav 4 S = 14 ) h r

y 5 = h (o)

₃

hs

5 T% tal distantato be oven ad E 24 km

Kemaining distone X

dhstanle Covexed by him 2x + * 24

1 6 5

4 wile Covenng a distante o R4 km, a

2 24 7

man

notiCed tthat ot

^ter

walkia 7 t o r for

7 = 4 l m

dictanta Covered by him c2x1L4 =lok

hour ho minutes tre dsfan ta Covered by

(11)

classmate

Date

Page

" dastamee Covered by hirn= lokm

Eime laken Cover 4tm hr

. Spoed z e/r

time takan to Coverzn

₃

s

3

G / h r

time Xake o Cover 5km h r

6 *ooo s e c

36 oo

tlaelakam o Cover km hs

s e c = s e c

5) Peter Can Cover

^a

Cetan distana

ⁱ

hYs

hrs Ihr 24

^{m i}

Ihr 24min by Covenng two-th'rd of the

dis kamte a t 4 km/hy md the rust at skm/^r.

Find He total dsame.

S lchor To tal o ' s tane = k n

3D

Speed for 2x 4 Kn

5km/hr 30

8 4 3 6

CAxKpee 2Pt 6kms

(12)

(To

^eiasSmAte

6 6Amar havelled rem e llage t the

Pest-o ice at he Aate s k p h ant

4km ph .

d t nl ked back at He vale

Aokm Hie lole jouiiney leck 5 heus 48 nminutes

s tane t t ost-off te om Total d's tante Covexed h o kmn itance Lhute Po 4Villa5 20

Av Specd 2 TAn aevoplaue lis alory theour Sds

f c Aq Laie a tlu Specds q 2ee, 4 oo,60

and 8co E n d t e average Spesd blana nd u eld.

ime toaken

vagek po 4 po bvl

(S+

5 h s 4 8 mins

60

D3pecd s ea bn/hr

In lhr dst. Coveved ?ooem

Spud

vok ou'ct tover in h r

Xlen i s t . Covesd in x hs 200

29 2/5

200

(13)

(12

_classMate

pats

Side Xm Ovened in

₂₀₀ Pag

A omd B

^{n e}

tuop Atationg 390 km apat 2 Sde «km ms Coverd în hs

von

^al

loa. and thav

3 Sida kms Covered in

600

1o wards

^B

at 65krn/%r Arottus tha'n slati

Sde x ku Covered 'n h s

70 B at

l a m m d

thavolk

4)k ms Coveed tn 200 35 km/hy A t w h a t tima do ttey

oln A B

4 kms Coveved 6X + u*+3" A

sloam 65

h s

25 h l e y mect at

400

ⁿ

h (AB) tnavelt 65 Em

aist D h AB tava (Lsx)km

Spaed time

n h BA thavels 35 km

e

T(a-1) hs BA thavels (35a)

Tota dstesmte 390 cm

1400

65 t 3s (x-1) 31o

Speed

^s

384

²

m/r

(14)

(

_clasSmate

65Y+3Sa S ^Date

Page

Pvblems on Tains

oo

390+ 3 5

Fox mu ae

360o

2X 36oo k /

o0o

. 25 h 3. Time akan a t a i n g lengthlmatu

rain AG fasts at o an to_PaSs_a pole r a Alanlivg rotzn Dra

thtn i+ meets a tAain BA a t Si2nal poS ie5 a t t l e b i e Taken

2.25 las P

^m

metre

Cover dlente.

h 25x60) hs

A Laken hy atrain 4lengh do

^{m z i a}

4 5 r b ) h _pass Aota Siationay Ohject q legt

2.15 Pm b oek r s i isHhe i m a a k n by ha irain

la Corzx (ltb) metrs.

Snppose tworains or kso bodi a2

u Same

movi'n9

d

(15)

15) 16 h

vnd Vm/s, WheA

^u>V

, the

t l e r r

Yelah ve specd (u-vm/s d A veepec h'velj ben abo 7

b o o i

v a . 6 Supp ose

Two thauw ^br

1wo Aspaad Bspad

movina ⁱⁿ

H oppoile direth'ons at nls

Cvnd

V / s

^, ^hen

heiv

hulakve

Speed

ProblomS

=

ut V) m/ A train toom lo

unning at he

Spoed of 30km/hr Eird the tima Tbkan

man Standvg near

7. 4tvo thaivs lnat a a metrt om d

In

OPpoSi he

^orechon

taken

moving

0 Yailway line.

b m e t t s a n

at ums

^{m d}

vVm/s then ti me

t thal ns

^Crass ^Lah ^utV

100 krn

1000

.D4 tnais 9 lenat m e t r e s md

0 . 1 km

T e akonto lonar passTime tRo fo

Cavar u

^D.l^Ko

bmetres o n movin in

the Same

oive chon at

^u

m n d Vm/s, Bren

^Bhe

Aima Laken by ta aster tnaxn 6

^Cavss

SlousortAain == ) Sac.

t Stadiing man Speed 30km

Time faleen to Covar 3okm h r r

4. Pt two tnaiug or bodies) stast at the

a m a Tme

O Poins A n d B Time alento lover o.1 m r D.1)hr

towards ach o tur and after Crossi 30

wy Aake

^a

md b lec

^In

veachin B

⁵⁰⁰

(16)

h (ov) x 36oo Secs

7 16 cassMAte

300 300 3Anan Standina A.

=12Secs hich i Rom_long He inds Liaat o Ésain

Crosses Hae bidg lnie lecands but hiesal.

) A tAain is moving

^{a t}

a Speed g /32km/r

2 t lngh4 t thain

ⁱ tto matru,

in 8Seconds End ti lenath ak tie baain

uo long will

^t ^Aake

fo Cruss

^a

railva platform

wa

tres levj? and i Åpe

ed.

t65

L e t h e

lehi tiaia

m e t Y e s

Tirne takem ts Cover Tme taun 20 S4CS

H platform t Cos

(to tl6S) mts

i m e

l a k e u L

oveY Xt 2 ) m_

Tme falkem to Cover Secs Specd

^{t t u} ^tAci'n

32 km coVred in h r time

15 o r 225 lo00 bCovevad i 132 x215

215 hs 8 18o)

^20X

132 rooo

hS hs

32 140 48

1

m

3 6 0 0

^Secs

30. ecs T Se cs,

²

(17)

eiassmate

2 n

of 59km/hr.

^Lulat

lme w f

L A i a t

a m a LOlio

he dection 5 /se c

Y

A

3al

Specd

^of

the rain lative -{5147)%

A Eaain 5 m o

man J

me

66 mh

t h a t Speed of 68 kmph

8 Emph

tAain

a t

m in

e &ane diveckion

ⁱⁿ tohieh Ehe 000

20

m

2 2 0 m

Speed Specd of t tie tiain Yelatve-(68-s)k

to man =(68-s)t tine

220 em

6 o km/hr

220 T Speed ime

tim

o00 66

hr ime An hys

300

3600 SacS tim

= 36oo

Se es

⁼

1 Secs 300

2 Se ccS

(18)

lassmate Oo m e t r e s

long takes 6

^Socs

Wal ki'ng a t 5 Emph

Date

Page

6 A Evain

fo Coss a man

60

in a directiom

oppos: te to h a t oP

he tvain. Find the speed of the trun 36

550 360 kcn

0 0 0

Ioln

36

ket

^the

Speed of the

t r a i n ⁼

2ed of ts auna 55 Em/

8pecd 9 tte

^{m a n}⁼

5 km/

5loO0 m/ls

36 oo

36 s

Speed of tletaain Ye lahive to mans

-

(36x +5D m/s

36 Speed_dst

time

36 + 5

36 6

36X50 O x 36

3645V 60o

36x = 5 5 0

550 36 m/s

X =