Question

A started a work and left after working for 3 days. Then B was called and he finished the work in ????????$\frac{1}{2}$ days. Had a left the work after working for ????$\frac{1}{2}$days, B would have finished the remaining work in 9 days. In how many days can each of them, working alone, finish the whole work?
(a) 7.5 days, 22.5 days
(b) 7 days, 9 days
(c) 5 days, 15 days
(d) 23.5 days, 8.5 days
(e) None of these

Answer 1

the correct answer would be no c

Answer 2

Answer:

Answer A.

A can finish in 7.5 days and B can finish in 22.5 days

Step-by-step explanation:

The question is here with correct numbers.  

A started a work and left after working for 3 days. Then B was called and he finished the work in 13 (1/2) days. Had a left the work after working for 4 (1/2) days, B would have finished the remaining work in 9 days. In how many days can each of them, working alone, finish the whole work?

Let A finish the work in X number of days and B can finish in Y number of days, if they work alone.  

A single day work = 1/X

B single day work = 1/Y.

Total work is done by A for 3 days and B finished the work in 13.5 days.

Thus we get equation 1 as below

3/X + 13.5/Y = 1

3/X + 27/2Y = 1 ------------------------------------E1

If A left the work after 4.5 days, B can finish in 9 days.

We get Equation 2 from above statement as below

4.5/X + 9/Y = 1

9/2X + 9/Y = 1 ----------------------------------------E2

Multiply E2 with 3/2 we get E3 as below

27/4X + 27/2Y = 3/2 --------------------E3

E1 – E3 gives us

3/X – 27/4X = 1 – 3/2

-15/4X = -1/2

4X = 30 or X = 7.5 days.

Substituting X value in E1, we get

27/2Y = 1 – 2/5 = 3/5

2Y = 27 * 5/3 = 45 or Y = 22.5 days