# 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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## [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)’

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## Question

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## 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?

This question was previously asked in

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96 90 92 94

## Answer (Detailed Solution Below)

Option 1 : 96

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## Detailed Solution

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**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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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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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.

If you agree with me please upvote me and follow me.

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

Now add above three equations

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

ANSWER is :- 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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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 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 ?

**A**

## 120 days

**B**

## 150 days

**C**

## 180 days

**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

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