Question

3. A can do a job in 4 whole 1/2 days, and B in 9 days.
(1) How long will they take to complete the job together?
(ii) If they are paid 3900 for the job, what will be each person's share?​

Answer 1

Given :-

• A can do a job in = 4(1/2) Days. = (9/2) days.
• B can do same job in = 9 days.

To find :-

• i) How long will they take to complete the job together ?
• ii) If they are paid 3900 for the job, what will be each person's share ?

Solution :-

→ LCM of (9/2) & 9 = 9 unit = Let Total work .

So,

→ Efficiency of A = ( Total work) / (Total Time taken by A alone) = 9 / (9/2) = 9 * (2/9) = 2 Unit / day.

→ Efficiency of B = ( Total work) / (Total Time taken by A alone) = 9 / 9 = 1 Unit / day.

Hence,

→ Efficiency of (A + B) = 2 + 1 = 3 unit / day.

Therefore,

→ Time Taken by Both of Them To complete whole work = 9/3 = 3 Days..(Ans i)

Hence, They take 3 days to complete the job together..

_________________

Now, we know That, Salary of workers is Given in The Ratio of Their Efficiency .

→ Efficiency of A = 2 unit/day.

→ Efficiency of B = 1 unit / day.

So,

→ A share : B share = 2 : 1

Let A share is 2x & B share is x .

Than,

→ 2x + x = 3900

→ 3x = 3900

→ x = 1300

Hence,

→ A share = 2x = 2*1300 = Rs.2600

→ B share = x = 1*1300 = Rs.1300. (Ans ii)

Therefore, Share of A & B are Rs,2600 & Rs.1300 Respectively.

Answer 2

i)time taken by A to do the job =9/2days

work it will do in one day=1/(9/2)=2/9

Time taken by B,to do the whole work=9days

work in one day=1/9

work done in one day by A and B together=2/9 +1/9=3/9=1/3

so,time they will take to complete the whole work together=3days

ii)each person will share acccording to their work

Work done by A in these three days,=2/9 ×3=2/3

work done by B in these three days=(1/9)×3=1/3

share of A=2/3 ×3900=2600

share of A=2/3 ×3900=2600share of B=1/3 ×3900=1300