notes and problems on time & work

7/27/2019 Notes and problems on Time & Work

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KQuabity Kgudatioj Tystkf

Wifk & \or`

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\or` to ck gojk is lkjkrabby dojsigkrkg as ojk

ujit. It fay ck dojstrudtijl or paijtijl a nousk,hibbijl up or kfptyijl a taj`, rkskrvoir or a distkrj.

\or`


3/12



Ih A daj go a pikdk oh wor` ij j gays, tnkj A's 1 gay'swor` 61/j

IhA's 1 gay's wor` 61/j, tnkj A daj hijisn tnk wor` ij

j gays.

\or` ajg fkj ark girkdtby proportiojab to kadn

otnkr i.k, ih tnk wor` ijdrkasks, tnk jo. oh fkjrkquirkg to go it, abso ijdrkasks, ih tnk wor` is to ck

dofpbktkg ij tnk safk jufckr oh gays.

Ifportajt Jotks


4/12



Fkj ajg gays ark ijvkrskby proportiojab, ik, ih tnkjufckr oh fkj ijdrkasks, tnk jufckr oh gays

rkquirkg to dofpbktk tnk safk wor` gkdrkasks

ajg vidk vkrsa.

\or` ajg gays ark girkdtby proportiojab, ik, ih tnk

wor` ijdrkasks, tnk jufckr oh gays rkquirkg abso

ijdrkasks, ih tnk wor` is to ck dofpbktkg witn tnk

safk jufckr oh fkj ajg vidk vkrsa.


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Ih A abojk dofpbktks sofk wor` ij x gays ajg C

abojk dofpbktks safk wor` ij y gays 0 tnkj A & C

daj hijisn tolktnkr wor` ij t gays

Kquatioj (1)

Ih A is x tifks as loog a wor`faj as C, tnkj=Satio

oh wor` gojk cy A ajg C 6 x = 1.

Satio oh tifks ta`kj cy A ajg C to hijisn a wor` 6

1 = x ..Kquatioj (3)
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1. Ih a pipk daj hibb a taj` ij x nour, tnkj tnk part hibbkg

ij 1 n 6 1 /x

3. Ih a pipk daj kfpty a taj` ij c nour, tnkj tnk partoh tnk hubb taj` kfptikg ij 1 n 6 1 / y

4. Ih a pipk daj hibb a taj` ij x nour ajg ajotnkr pipk

daj kfpty tnk hubb taj` ij y nour, tnkj tnk jkt parthibbkg ij 1 n, wnkj cotn tnk pipks ark opkjkg 6

(1/x) (1/y)..............Kquatioj (4)

Uipk ajg Distkrj


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Q1 = Twafi ajg Sama daj go a moc abojk ij 15 gays

ajg 75 gays rkspkdtivkby. Ij now fajy gays tnk moc

wibb ck hijisnkg, ih tnky wor` tolktnkr ?

Tobutioj=

Gays ta`kj cy swafi (x) 6 15 0 Gays ta`kj cy Sama (y) 675

Gays ta`kj ih tnky wor` tolktnkr 6t (1/15 )+ (1/75) 6

(1/t)....................ahtkr appbyijl Kquatioj (1)

t6 >

To tifk ta`kj to dofpbktk tnk wor` hor Twafi & Sama tolktnkr

is > gays.

Kxafpbks


8/12



Q3= Saf ajg Taf daj go a pikdk oh wor` ij 15 gays

ajg 1; gays rkspkdtivkby. Wnky wor` tolktnkr hor 4

gays ajg tnkj Taf bkavks. Saf hijisnks tnkrkfaijijl wor` abojk. Ij now fajy gays ij tnk totab

wor` hijisnkg?

Tobutioj =

Saf's 1 gay wor` = 1/15

Taf's 1 gay wor` = 1/1;

(Saf + Taf)'s 1 gay wor` = (1/15)+(1/1;)61/8(Saf + Taf)'s 4 gay wor` = 4/8

Skfaijijl wor` 6 1- (1/3) 6 1/3

To gays ta`kj cy Saf to dofpbktk 1/3 wor` 6 15/3 6 ; gays


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Q4=A is tnridk as loog as wor`faj as C ajg tnkrkhork

is acbk to hijisn a moc ij 85 gays bkss tnaj C. \or`ijl

tolktnkr, tnky daj go it ij now fajy gays ?

Tobutioj =Satio oh tifks ta`kj cy A ajg C 6 1 = 4.

Gihhkrkjdk oh tifk cktwkkj tnkf is 85 gaysTo tifk ta`kj cy C 6 4/3 75 6 85 gays

To tifk ta`kj cy A 6 35 gays

ih A & C wor` tolktnkr tnkj tifk ta`kj 6 (35

85)/(35+85).............appby kquatioj (1)

Wifk ta`kj to dofpbktk wor` ih tnky wor` tolktnkr is 61; gays


10/12



Q7= Uipk A daj hibb a taj` ij 15 fij, pipk C ij 35 fij

ajg a bka` daj kfpty tnk taj` ij 75 fij. Ih abb oh

tnkf wor` tolktnkr, hijg tnk tifk ta`kj to hibb tnk

kfpty taj`?

Tobutioj= Livkj

(1/x)6(1/15 + 1/35)

(1/y) 6 1/75

Jkt part hibbkg ij 1 fij 6 (1/15 + 1/35 1/75) 6 >....appby

Kquatioj (4)

To, tnk kfpty taj` wibb ck hibbkg ij > fij.


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