Question

Rahul does half as much work as Sameer in three fourth of the time. If
both take 12 days to complete a job, how much time will Sameer alone
take?​

Answer 1

Answer:

Let time taken by B to complete work = 4x Then A can do 1/2 work in 3x time.

So time taken by A to complete work = 6x

Let total work = 12 x ( LCM of both)

efficiency of A = 2

Efficiency of B = 3

12x/5 = 18 ; So x = 15/2

Total work = 12*15/2 = 90

Time taken by B to do it = 90/3 = 30 days

Let the number of days taken by B alone to finish the work be x.

So number of days taken by A alone to finish half of the work = 3x/4.

So number of days taken by A alone to finish the work = 2 × (3x/4)= 3x/2.

Number of days taken by both to find sh the work =18.

Pàrt of work done by both in 1 day = 1/18

Part of work done by A alone in 1 day =1/(3x/2) = 2/3x.

Part of work done by B alone in 1 day = 1/x.

So 1/x + 2/3x = 1/18 => (3+2)/3x = 1/18

5/3x = 1/18 => 3x = 5×18 => x = 5×18/3= 30

So number of days taken by B alone = 30