Question

A and B can do a work in 45 and 40 days respectively. They began the work together, but A left after some time and B finishes the remaining work in 23 days. After how many days did A leave?
1. 8 days
2. 7 days
3. 6 days
4. 9 days

Answer 1

Correct Answer - Option 4 : 9 days

Given:

A does one work in 45 days

B does one work in 40 days

Concept used:

If a person does work in 'n' days then one day work by a person is (1/n) part of total work.

Calculation:

Let them together work for x days and after x days A left the work 

A's one day work = 1/45

B's one day work = 1/40

The total work for one day when they work together = A's one day work + B's one day work 

⇒ (1/45) + (1/40)

⇒ (8 + 9)/360

⇒ 17/360 part

Then for x days their total work = (17/360) × x

⇒ 17x/360

Now remaining work = 1 - (17x/360)

⇒ (360 - 17x)/360      ----(i)

But this remaining work is completed by B in 23 days then,

And B's 23 days work = 23/40      ----(ii)

From equation (i) and equation (ii) we get,

(360 - 17x)/360 = 23/40

⇒ 360 - 17x = (23/40) × 360

⇒ 360 - 17x = 23 × 9

⇒ 17x = 360 - 207

⇒ 17x = 153

⇒ x = 153/17

⇒ x = 9 days   

∴ A leave after 9 days.