Question

A can do a piece of work in 40 days and B in 45 days. they work together for 10 days and then B goes away .In how many days will A finish the remaing work.​

Answer 1

Answer:

Step-by-step explanation:

A —40

B—45

Here LCM is total work

Hence Lcm (40,45)= (8x5, 9x5)=8x9x5=360

A’s one day work is 360/40=9 unit

B’s one day work is 360/45=8 unit

in 10 days A does 90 unit and B does 80 units

total work completed is 90+80=170

remaining work is 360–170=190units

A’s one day work 9 unit

so for 190 units he need 190/9 days or 21 and 1/2 days

Answer 2

Answer:

190/9 days

Step-by-step explanation:

A takes 40 days to complete the work

=> Fraction of work done by A in one day = 1/40

B takes 45 days to complete the work

=> Fraction of work done by B in one day = 1/45

If they work together for 1 day, they will complete (1/40 + 1/45) of the work

Fraction of work completed by (A+B) in 1 day = 1/40 + 1/45

= 9/360 + 8/360

= 17/360

Fraction of work completed by (A+B) in 10 days = 10*(17/360) = 170/360

Fraction of work left incomplete = 1 - 170/360 = 190/360

Now,

B goes away and A is left alone.

A needs to complete 190/360 of the work

We know that A completes 1/40 of the work in 1 day

We have to find "x" so that A completes (190/360) of the work in x days

Using ratio and proportion, we get:

x = (190/360) ÷ (1/40)

  = (190/360)*40

  = 190/9

The number  of days that A will take to complete the work (after B has left) is 190/9 or  $21\frac{1}{9}$