## A and B separately do a work in 10 and 15 days respectively. They worked together for some days and then A completed the remaining wor

Question

A and B separately do a work in 10 and 15 days respectively. They worked together
for some days and then A completed the remaining work in 5 days. For how many
days had A and B worked together?

in progress 0
2 weeks 2021-09-07T11:41:34+00:00 1 Answer 0 views 0

Answer to this problem is 3 days.

There are three methods to solve this problem.

Method-1 Fraction Method

A completes the work in 10 days -> In 1 day he completes 1/10 part of job.

B completes the work in 15 days -> In 1 day he completes 1/15 part of job.

Work done by A & B both in 1 day= 1/10 + 1/15

=(10+15)/(10×15) = 25/150 = 1/6

Let both A & B workd for ‘x’ days.

Work done by them in x day = x/6

Remaining work = 1-x/6 ………(1)

This remaining work is done by A alone in 5 days.

Hence,

Work done by A in 5 days = Remaining work

5/10 = 1-x/6 …. From (1)

x/6 = 1–1/2

x = 6*1/2

x=3

A & B worked for 3 days.

Method-2 LCM Method

Let the total units of work be LCM(10,15)=3

A does 30/10 = 3 units per day work

B does 30/15 = 2 units per day work

Together they do (3+2)=5 units of per day work.

Let say both of them worked for x days.

Work done by them in x days = 5x

Remaining work = 30–5x

This remaining work done by A alone in 5 days

Hence,

5*(A’s work per day)= 30–5x

5*3=30–5x

x=3

A & B worked for 3 days.

Method-3 Percentage Method

Let the total work be 100%

A does 100/10 = 10% work in 1 day

B does 100/15 = 6.66% work in 1 day

Both A & B do (10+6.66)=16.66% work in 1 day

Let say they worked for ‘x’ days

In x days the complete x*16.66% work.

Remaining work = 100%-x*16.66%

This remaining work completed by A alone in 5 days

Work done by A in 5 days = 5*10%= 50%

Hence,

Remaining work = work done by A in 5 days

100 – x*16.66%=50%

x*16.66% = 100%–50%

x*16.66% = 50%

x = 50/16.66

x=3 days

A & B worked for 3 days.