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# a and b can do a piece of work in 60 days, b and c can do it in 100 days, a and c can do it in 75 days. in how many days b alone can do it?

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### Mohammed

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## [Solved] A and B can complete a work in 60 days, B and C complete it

Given: A + B can complete in 60 Days B + C can complete in 80 Days C + A can complete in 120 Days Calculation: Taking LCM, total work = 240 (A + B)’ Home Quantitative Aptitude Time and Work Work Efficiency

## A and B can complete a work in 60 days, B and C complete it in 80 days, C and A can complete the same work in 120 days. In how many days, B alone can do that work?

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TSPSC Group 4 Secretarial Ability Official Paper-II (Held in: 2018)

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96 90 92 94

Option 1 : 96

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## Detailed Solution

Given:

A + B can complete in 60 Days

B + C can complete in 80 Days

C + A can complete in 120 Days

Calculation:

Taking LCM, total work = 240

(A + B)’s 1 day work = 240/60 = 4      ---- (1)

(B + C)’s 1 day work = 240/80 = 3      ---- (2)

(C + A)’s 1 day work = 240/120 = 2      ---- (3)

Now, add equation 1 and 2 then subtract 3 from it to get 2 × B’s 1 day work

⇒ 4 + 3 – 2 = 5 ⇒ 2B = 5 ⇒ B = 5/2 = 2.5

∴ Number of days required = 240/2.5 = 96

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Last updated on Feb 3, 2023

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स्रोत : testbook.com

## A and B can complete a work in 60 days, B and C can complete it in 80 days, C and A can complete the same work in 120 days. In how many days, B alone, can do that work?

Answer (1 of 9): Solution of the given problem is shown below, * Let W denotes the whole given work. * It is mentioned that * * (i) A & B can complete the work W in 60 days. * (ii) B & C can complete the work W in 80 days. * (iii) C & A can complete the same work in 120 days. * (iv) Let ... A and B can complete a work in 60 days, B and C can complete it in 80 days, C and A can complete the same work in 120 days. In how many days, B alone, can do that work?

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Absolutely not Definitely yes Related questions

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Sanjay

Let's share our knowledge Author has 118 answers and 6.2K answer viewsFeb 3

Let's solve the problem……..

(A+B)=60=1/60 (B+C)=80=1/80 (C+A)=120=1/120 Now

(A+B)+(B+C)+(C+A)=1/60+1/80+1/120

Or, (2A+2B+2C)=(4+3+2)/240

Or, 2(A+B+C)=9/240

Or, (A+B+C)=3/(80×2)

Or, (A+B+C)=3/160 Now……

(A+B+C)—(C+A)=3/160–1/120

Or B=(9–4)/480 Or, B = 5/480 Or, B = 1/96

So B can finish the work in 96 days.

Gaurav Pipil

B.Tech in in Computer Science, Gautam Buddha University (Graduated 2016)4y

lets assume total amount of work is 240 units.

A+B one day work will be => 240/60 = 4 units

B+C one day work will be => 240/80 = 3 units

C+A one day work will be => 240/120 = 2 units

A+B+B+C+C+A = 4 + 3 + 2

2(A+B+C) = 9 A + B + C = 9/2

put the value of A + C in above equation

2 + B = 9/2 B = 5/2

B alone can do the work in 240/(5/2) = 96 days

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Ved Prakash Sharma

Former Lecturer at Sbm Inter College, Rishikesh (1971–2007)Author has 12.1K answers and 12.1M answer views4y

let A alone can do a piece of work in x days, B alone in y days. and C alone in

z days. therefore their one day work will be 1/x,1/y and 1/z respectively.

Accordingly:-

1/x+1/y= 1/60…………….(1)

1/y+1/z= 1/80……………..(2)

1/z +1/x=1/120………………(3)

On adding eqn.(1). (2) and (3).

2.(1/x+1/y+1/z) =(4+3+2)/240=9/240 = 3/80

1/x+1/y+1/z=3/160……………(4)

On subtracting eqn.(3) from (4)

1/y =3/160–1/120 =(9–4)/480=5/480 = 1/96

1/y=1/96 or. y = 96 days

B alone can do that work in 96 days. Answer.

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स्रोत : www.quora.com

## A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it ?

Click here👆to get an answer to your question ✍️ A and B can do a piece of work in 72 days. B and C can do it in 120 days. A and C can do it in 90 days. In what time can A alone do it ? Question

A

B

C

D

## 200 days

Medium Open in App Solution Verified by Toppr

Correct option is A)

(A + B)'s 1 days' work =

72 1 ​ ;

(B + C)'s 1 days work =

120 1 ​ ;

(A + C)'s 1 days' work =

90 1 ​ ∴(A+B) ′ s+(B+C) ′ s+(A+C) ′ s 1 days work = 72 1 ​ + 120 1 ​ + 90 1 ​ = 360 5+3+4 ​ = 360 12 ​ = 30 1 ​ ⇒2(A+B+C) ′ s 1 days' work = 30 1 ​ ⇒(A+B+C) ′ s = 60 1 ​

∴ A's 1 days' work = (A+B+C)'s 1 days' work - (B+C)'s 1 days' work

= 60 1 ​ − 120 1 ​ = 120 2−1 ​ = 120 1 ​

∴ A alone will complete the work in 120 days