Question

If 25% of a certain work is done by a and after that remaining was done by b, the work will be completed in 20 days. if 75% of the work is done by a and the remaining is done by b, the work will be completed in 30 days. if a and b work together, in how many days work will be completed

Answer 1

Solution:-

Using the formula : Work = Rate*Time

Time = Work/Rate

Assuming A's rate of work as 'A'

Assuming B's rate of work as 'B'

A does 25 % of the work, so A did 25/100 = 0.25 part of the work.

B does 75 % of the work, so A did 75/100 = 0.75 part of the work.

Days for which A worked + Days for which B worked = Total Days 

Work of A/Rate of A + Work of B/Rate of B = Total Days

Situation 1 -

0.25/A + 0.75/B = 20

Multiplying the above by 12, we get.

⇒ 3/A + 9/B = 240  .....................(1)

Situation 2 -

0.75/A + 0.25/B = 30 

Multiplying the above by 4, we get.

3/A + 1/B = 120 .......... (2)

Subtracting (2) from (1), we get.

   3/A + 9/B = 240
   3/A + 1/B = 120
 -        -        -
________________
            8/B = 120
________________

⇒ 8/B = 120

⇒ 120B = 8

⇒ B = 8/120

⇒ B = 1/15

Now, Substituting B = 1/15 in (2)

⇒3/A + 1/B = 120

⇒ 3/A + 1÷1/15 = 120

⇒ 3/A + 1*15 = 120

⇒ 3/A + 15 = 120

⇒ 3/A = 120 - 15

⇒ 3/A = 105

⇒ 105A = 3

⇒ A = 3/105

⇒ A = 1/35

Now, combined rate = 1/15 + 1/35

Taking L.C.M. of the denominator and then solving it.

⇒ (7 + 3)/105

⇒ 10/105

Time taken when working together = 105/10

⇒ 21/2

⇒ 10 1/2 days

Hence, if A and B work together, the work will be completed in 10 1/2 days.

Answer.