time and work

Black holes of Aptitude-Time and Work

©Mayan Gupt &Shahnawaz Alam- [email protected]

Time and Work

Type I

Exp 1 Rizwan can do a piece of work in 6 days and Payam can do the same work in 8 days,working together ,in

how many days they will complete the same work:

Solution:

Step I Take the L.C.M(6,8) of number of days taken by R and P alone to complete the work

Imagine there are 24 bricks(Total work) in total ,R can transfer all bricks in 6 days from one place to

other, So he will have to pick 4 bricks a day and P will have to pick 3 bricks a day.

R -6 4(24/6)

L.C.M(6,8)=24

P-8 3(24/8)

Step II if P and R work together they will pick 7 bricks/day.

Step III They can pick all 24 bricks in

=24

7 days =

𝑇𝑜𝑡𝑎𝑙 𝐵𝑟𝑖𝑘𝑠

𝑁𝑜 𝑜𝑓 𝑏𝑟𝑖𝑐𝑘𝑠 𝑝𝑖𝑐𝑘𝑒𝑑 /𝑑𝑎𝑦

Type II

Exp 2 Gulfshan and Maryam working together can do a piece of work in 8 days. If Gulfshan alone can do it in

24 days, in How many days Maryam alone can complete the same work?

Solution:

G+M-8 3(24/8)

L.C.M (8, 24) =24

G-24 1(24/24)

M alone can pick =2(3-1) bricks/day.

So Maryam alone can do the same work in

= 12 =24

2 days =





Type III

Exp 3 If Afshan and Sahir can do a work in 18 days and 24 days respectively. They worked together

for 8 days and then Afshan left. The remaining work was finished by Sahir in How many days?

Solution:

A-18 4(72/18)

L.C.M (18, 24)=72

S-24 3(72/24)

Step I A+S can pick 7(4+3) bricks/day.

Step II They worked for 8 days so, they will pick 56(8*7(4+3)) bricks in 8 days.

Step III Left over bricks 16(72-56)

Step IV B will pick remaining 16 bricks in 16/3 days.

Type IV

Exp 4:Sajid can do a piece of work in 18 days and Haider in 12 days. They began the work together, But Haider

left the work 3 days before its completion. In How many days in all was the work completed?

Solution:

S-18 2(36/18)

L.C.M (18, 12)=36

H-12 3(36/12)

Let say work was finished in N days ,So S worked for N days and H worked for X-3 days ,together they have to

pick 36 bricks.



Total Bricks=no of days S worked×S can pick bricks/day+no of days H worked×H can pick bricks/day

36=N×2+ (N-3)×3

N= 9days

Shortcut:

H didn’t work for 3 days, so those extra bricks 9(3×3) will be added to total bricks

So your answer will be

36+9/5(3+2)

9 days

Type V

Exp 5:Shabnam and Ayesha together can complete a work in 15 days. Shabnam is 50 % more efficient worker

than Ayesha. How long Shabnam will take to complete the work alone?

Solution:

If S is 50% more efficient worker, She will Pick 150 Bricks and A will pick 100 Bricks in a day.

S=150 bricks

A=100 bricks

S+A=250 bricks

If they can finish the work in 15 days and can pick 250 bricks in a day, there would have been 250×15 bricks in

total. Which can be picked by S in

=𝑇𝑜𝑡𝑎𝑙 𝐵𝑟𝑖𝑘𝑠

𝑁𝑜 𝑜𝑓 𝑏𝑟𝑖𝑐𝑘𝑠 𝑝𝑖𝑐𝑘𝑒𝑑 /𝑑𝑎𝑦 =

250×15

150= 25 𝑑𝑎𝑦𝑠

Type VI

Exp6:Ashba does 4/5 of a piece of work in 20 days, She then calls in Asra and they finish the remaining work in

3 days. How long Asra alone will take to do the whole work?

Solution:

Ah =4

5 work 20 days

Full work (1) 20×5

4=25 days

Ah+Ar1= 1-4

5=

1

5 3 days

Full work (1) 3×5

1 =15 days



Ah+Ar -15 5(75/15)

L.C.M (15, 25)=75

Ah-25 3(75/25)

M alone can pick =2(5-3) bricks/day.

So Maryam alone can do the same work in

=75

2 days =



VII

Exp7:If Manal can do a piece of work in 12 days and Najam can do it in 15 days. How many days it will take to

complete the same work, If they work alternatively starting from Manal:

Solution: 5(60/12)

M 12 60(L.C.M (12, 15))

N 14 4(60/15)

Since they are working on alternate days, so they will pick 9(5+4) bricks in 2 days.

Days bricks

2 9

Now we will multiply bricks with a NUMBER which will make bricks near to total bricks (60), but not greater

than 60, and we will multiply days with the same number.

Days bricks

2 ×6 9×6(54)

Now we are left with 6 bricks, since M has started work, now again its M’s turn after 12 days work.

Days bricks

12 54

+1 +5

13 59



Now its N’s turn and we are left with 1 brick, which can be picked by N in ¼ days.

=𝑛𝑜 𝑜𝑓 𝑏𝑟𝑖𝑐𝑘𝑠 𝑛𝑒𝑒𝑑 𝑡𝑜 𝑏𝑒 𝑝𝑖𝑐𝑘𝑒𝑑

𝑛𝑜 𝑜𝑓 𝑏𝑟𝑖𝑐𝑘𝑠 𝑐𝑎𝑛 𝑏𝑒 𝑝𝑖𝑐𝑘𝑒𝑑 𝑖𝑛 𝑎 𝑑𝑎𝑦

13+1/4 59+1=60 bricks

So work will be complete in 131

4 days.

TypeVIII

Exp 8: Manal and Najam can do a piece of work in 12 days, Najam and Ayesha can do it in 15 days, Manal and

Ayesha can do it in 20 days. how long it will take to complete the work, If they work together and alone?

Solution:

M+N 12 5(60/12)

N+A 15 60 [L.C.M (12, 15, 20)] 4(60/15)

M+A 20 3(60/20)

Since there is double counting of every one so we will multiply total bricks by 2.

M+N+A=2×60

5+4+3=10days

If we want to calculate it for M alone, we need to add bricks of those equations where M is present and

subtracted those where M is absent

2 × 60

5 − 4 + 3= 30 𝑑𝑎𝑦𝑠

Same for N and A

N alone

2 × 60

5 + 4 − 3= 20𝑑𝑎𝑦𝑠

A alone

2 × 60

4 + 3 − 5= 60𝑑𝑎𝑦𝑠



Type IX

A=X+t1

B=X+t2

A+B=X=√𝑡1 × 𝑡2

Exp9: If Manal takes 16 hrs more to complete the work than Manal and Asra take together to do the same work

and Asra takes 9 hrs more to do the same work than they together take. How many days it will take to finish the

work if they work together?

Solution:

According to formula

X=√𝑡1 × 𝑡2

X=√16 × 9

=12 days

Type X

Exp 10:If A Men or B women or C children can do a piece of work in N days, How Many days it will take to

complete the same work by D men and E women and F children:

1

𝐴𝑛𝑠=

1

𝑁 × (

𝐷

𝐴+𝐸

𝐵+𝐹

𝐶)

3M or 4 W can do a piece of work in 43 days then 7 M and 5 W will do it in how many days?

Solution:

1

𝐴𝑛𝑠=

1

𝑁 × (

𝐷

𝐴+𝐸

𝐵+𝐹

𝐶)

1

𝐴𝑛𝑠=

1

43 ×

7

3+

5

4 =

1

12

=12 days



Type XI

𝑀×𝐷×𝐻

𝑊=

𝑀1×𝐷1×𝐻1

𝑊1+

𝑀2×𝐷2×𝐻2

𝑊2+

𝑀3×𝐷3×𝐻3

𝑊3+……

Exp 11:If 40 men can finish a work in 60 days working 6 hrs a day, how long it will take to finish the double

work by 60 men working 8 hrs a day?

Solution:

𝑀 × 𝐷 × 𝐻

𝑊=

𝑀1 × 𝐷1 × 𝐻1

𝑊1

40 × 60 × 6

1=

60 × 𝐷1 × 8

2

=60 days

Exp12:A certain number of person can complete a piece of work in 55 days. If there were 6 person more, the

work could have been finished in 11 days less. How many person were originally there?

𝑀 × 𝐷 × 𝐻

𝑊=

𝑀1 × 𝐷1 × 𝐻1

𝑊1

𝑀 × 55

1=

(𝑀 + 6) × 44(55 − 11)

1

M=24 days

Type XII

Exp13:4 men and 6 women can complete the work in 8 days, While 3 men and 7 women can complete the work

in 10 days, In how many days will 10 women and 5 men will complete the same work?

[4M+6W=1

8]×8……………………………………(i)

[3M+7W=1

10]×10………………………………..(ii)

(i)=(ii)

32 M+48 W=30M+70W

1M=11W=M/W=11/1

Take M=1,W=1



We know that

𝑀 × 𝐷 × 𝐻

𝑊=

𝑀1 × 𝐷1 × 𝐻1

𝑊1

(4M+6W) ×8=(10W+5M)×D

(4×11+6×1) ×8=(10×1+5×11) ×D

D=80/13 days

time and work

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