TIME & WORK

TIME & WORK

1) Sabse pahle ek basic formula dekhe jo bade kam ka h…

M1*D1*T1*E1/W1 = M2*D2*T2*E2/W2

Yahan par M=men, D=days, T=time, E=efficiency, W=work

Humare ques me jo jo cheez h di formule me us us ka use kare baki chod de…

Ex- 38 men working 6 hours a day can do a wrk in 12 days. Find the number of days in which 57 men working 8 hrs a day can do twice wrk. Assume that 2 men of the 1st grup do as much wrk in 1 hr as 3 men of 2nd grup do in 3/2 hr.

Ab yahan dekhe….M1= 38, T1=6, D1=12, E1=2*1=2,W1=1

M2=57,T2=8,D2=?,E2=1.5*3=4.5,W2=2

W1=1 kyuki ek hi kam karte h, W2=2 kyuki twice kam karte h..put the value and solve it….D2= 27 ans

2) A 15 din me karta h ek kam aur B 12 din me….to A+B kitne din me karenge ?

old and main concept---- A 15 din me ek kam karta h to 1 din kam 1/15 same B ka ek din ka kam 1/12 to ab A+B ka ek din ka kam = 1/15 + 1/12 = 3/20

to pura kam karne me laga 20/3 days (1 din me karne me jo laga usi koreverse kar de ans aa gya..)

ye main concept h ise to pahle samjhe kyuki SSC me kuch tough ques aate h jinme trick nai hoti aap ko isi concept se karna hoga…

short method----

A = 15 4 (60/15)

60 +

B = 12 5

= 9

A+B = 60/9 = 20/3 ans

Dekho guys time and wrk chapter me mostly ques me hum LCM nikalte h then karte h…ab dekhe maine jaisa likha h waise hi aadat dale….A ka 15 aur B ka 12 to inka LCM 60 beech me likha…ab 15 ko 60me devide kiya to aaya 4 to use A ke samne likha…..same 4 B…unka total 4+5 kiya kyuki A+B nikalna h bas use LCM me devide kar diya…

Suppose kabi diya ho A=13, B=12 to aise case me aap LCM nikalne me tym na waste kare…aise me LCM 12*13 le le…turant…ans same aayega…waise ye tarika aap kahi bi laga sakte h…jaise ki upar wala hi ques phr se dekhe…

A= 15 12 (15*12/15)

15*12 +

B=12 15

= 27

A+B = 15*12/27 = 20/3 ans

Dono me ans same h…bas difference itna h mere hisab se ki 1st case me LCM calculate karna time taking jab ki 2nd case me last me unhe katna pitna h jo ki easy process h…rest ur choice…aur ye LCM wali trick specific LCM wale chapter me chod kar kahi bi laga lo….

3) A+B = 12, A = 15 to B=?

A+B= 12 5

60 -

A = 15 4

= 1

B= 60/1 = 60

Yahan humne 5-4 kiya kyu ki bhai logo agr A+B me se A ka minus karenge tbi to B ki value aayegi…

4) A=6, B=12, C=24 to A+B+C = ?

A=6 4

+

B=12 24 2

+

C=24 1

= 7

A+B+C = 24/7 ANS

5) A+B=12, B+C=15, C+A=20 to A,B,C = ?

A+B=12 5

+

B+C=15 60 4

+

C+A=20 3

= 12

(A+B+C) = 60*2/12 = 10 (2 se multiply isliye kiya h kyuki agr hum A+B, B+C, C+A ko add karenge to 2[A+B+C] milega aur hume nikalna h [A+B+C] ka)

6) A 3 times tez h kam karne me as compare to B…isliye A 60 din pahle hi kam khatm kar deta h as compare to B. to A+B=?

Ek chez to ye dekhe ki B-A=60 (total jitney din lagenge unka difference 60 h)

Ab dekhe---

A B

Capacity 3 1

Days 1 3 (but obvious h ki agr A ki capacity 3time h to use kam karne me kam din lagenge)

Ab maine upar btaya tha ki B-A=60

To dekhe 3-1 =60

To ab 2 = 60

To ab 1=60/2=30 (2 ki value 60 h to hume 1 ki value nikalni h)

To ab agr dhyan de ki----

A B

Capacity 3 1

Days 1 3

Real days 1*30=30 3*30=90

Means A 30 din to B 90 din me wok am kar payega ab A+B nikal le..

7) Agr 3M OR 4F kisi kam ko 43 days me kar sakte h to 7M AND 5F kitne din me karenge ?

Pahle to ek chez dhyan de jo bahut jaruri h ki diye hue case me OR use h aur qus wale case me AND . ye case bahut easy h karna…is trick samjh le…

(7/3 + 5/4)* Y = 43

Y= 12 ANS

Ab yaad rakhne ka tarika dekh le ki 7/3 aur 5/4 hi kaise?

Hume jitney ka nikalna h use upar likhenge aur jitney ka diya hua wo neche…matlb 7M ka nikalna h aur 3M ka given h to humne likha 7/3.

8) 12M + 16F = 5, 13M+24F=4 to 7M+10F = ?

Complicated case jo puch liya jata h…bade simple way me samjha raha hu samjhne ki koshish kare ---

12M+16F = 5 ……..(1)

13M+24F = 4………..(2)

Ab kya kare ki isme 5 aur 4 se unhi ki equation me left hand side multiply kar de…jis se right hand side 1 day ho jaye….kyuki ab ek me 5day aur dusre me 4day h to compare karne me muskil h….to multiply kiya to bana…

60M+80F = 1

52M+96F = 1

Absimple h right side same 1 ho gayi h to ab dono equation me M and F ka difference nikal le aur equal kar de…means

(60-52)M = (96-80)F

8M=16F

M=2F

Ab hum kya karenge ki M=2F ko use karte hue equation 1 or 2 ko and hume jiska nikalna h usko kisi ek me chahe M ya F me convert karenge..

Means eq1 = 12M+16F=5

24F+16F= 5 (M=2F to 12M will be 24F )

40F=5 ………..(3)

Given qus 7M+10F = ?

14F+10F =?

24F = ? ……..(4)

Ab apna formla use karenge---- > M1*D1*T1*E1/W1 = M2*D2*T2*E2/W2

Yahan sirf M and D h to baki sab chod de…

M1*D1=M2*D2

40*5=24*Y (eq 3 and 4 se )

Y=25/3 ANS

9) A ek kam ko 15 din aur B usi kam ko 10 din me kar sakte h….A ne 5 din kam kiya phr B bi aa gya to us kamko karne me kitne din lagenge…

Dekhe us kam ko kitne din lagenge hume ye nikalna h….maan lo ki X days lagenge…ab is X me A ne jo 5 din kam kiya wo aur phr A+B ne mil kar kam kiya suppose Y din wo dono hi included h..means X=5+Y (ye bas samjhane ke liye likha h)

Ab dekhe…A to suru se le kar end tak kam karta raha means agr humne mana h ki total X days lage to A ne total X days kam kiya…aur B 5 din bad aaya to B ne X-5 days kam kiya

Ab X/15 + (X-5)/10 = 1 (use old method mentioned in point 2)

X=9

10) A= 10, B=15 dono ne mil kar kam suru kiya but B kamkhatm hone ke 3 din pahle hi chala gya…is tarah kam khatm hone me kitne din lagenge?

Ab dekhe 3 din pahle B chala gya means ab jo us tym tak bachahua kam h wo A ko karna h aur akele matlb use 3 se jayda hi din lagenge …mana ki Y din….aur mana ki unho ne Z din take k sath kam kiya…ab mana X din me total kam khatm hoga….to X=Y+Z (ye bas samjhane ke liye likha h)

Ab dekhe total X din lage means A ne to pure X din kam kiya aur B 3 din pahle gya to usne X-3 din kiya

Isliye X/10 + (X-3)/15 =1

X=36/5 D

11) A=10, B=15, C=20…ab A aur B ne kam karna suru kiya..phr 5 din bad C bi unke sath aa gya..lekinkuch din sath kam karne ke bad B ko kisi vajah se 3 din pahle hi kam chod kar jana pada to ab A aur C ne akele kam kiya…to batao total kitne din lagenge….

Guys ye sab se tough case bana diya maine is se tough nai aa sakta bank me…

Suppose total X days lage kam karne me to sirf ek A ne jisne pure tym kiya to uske case me X hoga…B jo tha wo 3 din pahle chala gya to X-3 aur C 5 din bad aaya to X-5

Means X/10 + (X-3)/15 + (X-5)/20 = 1

Solve and find X…..

12) A+B=12, B+C=16. Ek kam ko pahle A 5 din karta h phr chala jata h then B 7 din tak karta h aur chala jata h phr C 13 din tak kam karke use khatm karta h…to C akele kitne din me kar payega wo kam?

A+B ka 1 din ka kam = 1/12 ……..(1)

B+C ka 1 din kam = 1/16……………(2)

Ab ques ke according---

A ka 5 din kam + B ka 7 din ka kam + C ka 13 din ka kam = 1 work

A’s 5 days work + B’s 5 days work + B’s 2 days work + C’s 2 days wrk + C’s 11 days wrk= 1

(humne B aur C ke wrk ko bas brk kar ke likha h)

(A+B)’s 5 days wrk + (B+C)’s2 days work + C’s 11 days wrk = 1 (pair bana lo ab)

5/12 + 7/16 + C’s 11 days wrk = 1 (use eq 1 & 2)

C’s 11 days wrk = 1- (5/12+7/16) = 11/24

Now C’s 1 day wrk = 11/(24*11) = 1/24

C can complete whole wrk in = 24 days

Agr A aur B ka nikalna hota to eq 1,2 ko use kare aur C ki value put kare…

13) To do a certain job B would take 3 times as long as A and C together and C take twice as long as A and B together. The A,B,C together can complete it in 10 days. Find A,B,C separate work..

3 times B daily wrk = (A+C)’s daily wrk

Add both side B’s daily wrk

4 times B daily wrk = (A+B+C)’s daily wrk

4 times B daily wrk = 1/10 (A,B,C can complete it in 10 days)

B’s daily wrk = 1/40

Dis u can find C’s daily wrk = 1/30

And using A+B+C = 10 days u can find A wrk..

14) A can complete a work in 15 days at 8hrs/day…B can complete that wrk in 20/3 days at 9hrs/day…agr A aur B dono ek sath daily 10hrs kam kare to kitne din tak ho payega?

A daily 8hr kam kare to kam 15 din me hoga

Means agr wo daily 1 hr kam kare to 15*8=120 din me complete hoga

Isi tarah B daily 1 hr kam kare to 20*9/3 = 60 days me hoga

Ye is liye kiya h kyuki ab dono 1 hr daily kam kar rahe h means base same ho gya to compare karna aasan ho gya…

Ab A+B nikal le…40 days aayega

Ek din me dono 10 hr kam karte h to is tarah 40/10 = 4 din lagenge…

15) Ek aadmi ne ek ghar 40 din me bana dene ka vayda kiya…usne 100 aadmi kam par lagaye…35 din bad 100 aadmi aur le aaya…aur tb ja kar kam ko fixed tym me khatm kar paya…agr wo extra 100 aadmi nai lata to wo kitne extra din aur leta kam karne ke liye…

Pahle 100 aadmi ne 35 din tak kam kiya..phr 200 aadmi ne 5 din tak kam kiya (40-35=5)

Mana ki 100 aadmi X din me kam kar lete…..to 100 aadmi ka 1 din ka kam = 1/X isi tarah 35 din ka kam = 35/X

Ab 200 aadmi ka dekhe…100 aadmi ka 1 din ka kam 1/X to 200 aadmi ka 1 din ka kam = 2/X………..to 200 aadmi ka 5 din ka kam 2*5/X

To eq bani---

To 35/X + 2*5/X = 1

X= 45 days

Matlb agr extra 100 na aate to 45 days me karte matlb 45-40 = 5 days aur extra lete ..ANS

16) Ek aadmi ne ek kam ko 150 din me pura karne ka theka liya….usne 20 male, 30 female, 75 boys ko kam par lagaya. Lekin 60 days bad usne dekha ki sirf ¼ kam hi pura hua h. ye dekh kar usne sari females ko aur 50 boys ko kam se nikal diya aur kuch males ko kam par laya…aisa karne par kam 5 din pahle hi khatm ho gya…ab agr ye maan le ki 3 male = 5 female and 2 female = 3 boys to batayie ki aadmi ne kitne extra males baad me bulaye?

Ab dekhe ki is ques ko kaise karna h….

Haahhahaha bhai ab khud bi kuch karo….ye ques jisne kar liya matlb usne ye chapter ache se samjh liya….

17) A ek kam ko 6 din B usi kam ko 5 din me kar leta h…agr dono ek sath kam kare aur unhe 220rs mile to usme dono ka alag alag share kitna hoga…?

Jab bi aise ques aaye jisme share nikalna ho to dhyan de isme hamesha unka 1 day ka wrk nikalte h…….

A ka 1 din ka kam 1/6

B ka 1 din ka kam 1/5

To 220 me unka share = 1/6:1/5 = 5:6

Means A ka share = 220*5/11 = 100rs