Question

A+B alternatively can do work in 17days and B+A alternatively can do a work in 69/4 days then find how many day's a and B will take to complete the work separately​

Answer 1

A will finish in 15 days & B will finish in 20 Days

Step-by-step explanation:

Let say A & B's 1 Day work are A  & B respectively

A+B alternatively can do work in 17days

=> A work for 9 days  & B work for 8 Days

=> 9A + 8B = Work

B+A alternatively can do a work in 69/4 days

=> B work for 9 days & A work for 33/4 Days

=> 9B + 33A/4 = Work

Equating both

=> 9A + 8B =  9B + 33A/4

=> B = 3A/4

=> 4B = 3A

9A + 8B  = work

=> 9A + 2(4B) = Work

=> 9A + 2(3A) = Work

=> 15A = work

A will finish in 15 days

9A + 8B = 3(3A) + 8B

= 3(4B) + 8B

= 20B

B will finish in 20 Days

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Answer 2

Question :---- A+B alternatively can do work in 17days and B+A alternatively can do a work in 69/4 days then find how many day's A and B will take to complete the work separately ?

Solution :---

it is given that A+B alternatively can do a work in 17 days.

That Means A work for 9 Days & B work for 8 Days. ( Since A start the work .)

Now, B+A alternatively can do a work in 69/4 = 17(1/4) days..

That Means B work for 9 days & A work for 8(1/4) Days..

( Since B Start the work this Time .)

Now, Let A one's day work = A

→ B one's day work = B

Since work is same in Both case..

→ 9A + 8B = 9B + (33/4)A

→ 9A - (33/4)A = 9B - 8B

→ (3/4) A = 1B

→ A/B = 4/3

So, Efficiency of A = 4 unit /day.

→ Efficiency of B = 3 unit /day.

So, Total work = 9A + 8B = 9*4 + 8*3 = 60 units..

So, A will complete the whole work in = 60/4 = 15 days.

→ B will complete the whole work in = 60/3 = 20 days..

Hence, A alone will Finish the whole work in 15 days, and B Alone will do the same work in 20 days..