Posted on - 03-02-2017

Bank PO

Work to be done is usually considered as one unit. It may be, constructing a wall or laying a road, filling up or emptying a tank or cistern or eating certain amount of food. If there is more than one person (or thing) carrying out the work, it is assumed that each person (or thing) does the same amount of work each day and all the persons (or things) do exactly the same amount of work. .

**For example: **

(i) If a person completes the work in 4 days, he does 1/4th of the work on each day and conversely, if a person can complete 1/4th of the work in one day, he can complete the work in 4 days. .

(ii) If
a tap can fill a tank in 20 minutes, then in one minute, it can fill 1/20^{th}
part of the tank. .

Wages earned by people doing a work together are to be distributed in the ratio of the total work done by each of them. If a group of people, working at different pace (i.e., the work done by each of them per day is different), start and complete a work together, then the wages or earnings have to be divided in the ratio of the work per day of each of them. .

Here, we follow what is known as “UNITARY METHOD”, i.e., the time taken per “Unit Work” or number of persons required to complete “Unit Work” or work completed by “Unit Person” in “Unit Time”, etc., is what is first calculated. .

For example, if 20 men take 30 days to complete a work, then we have

1 man can complete (1/20)th work in 30 days. .

1 man can complete (1/600)th work in 1 day. .

20 men can complete (1/30)th work in 1 day. .

600 men can complete 1 work in 1 day. .

1 man can complete 1 work in 600 days. .

We should recollect the fundamentals on variation (direct and inverse) here. .

- Work and men are directly proportional to each other, i.e., if the work increases, the number of men required to complete the work in the same number of days increases, and vice versa. .
- Men and days are inversely proportional, i.e., if the number of men increases, the number of days required to complete the same work decreases and vice-versa. .
- Work and days are directly proportional, i.e., if the work increases, the number of days required to complete the work with the same number of men also increases and vice versa. .

A can do a work in 21 days and B in 28 days. If they work together in how many days will they complete the work? .

In one day, A can do th of the work and B can do th of the work.

In one day they together can complete of the total work.

So they can complete the work in 12 days. .

A can do a work in 12 days, with the help of B he can do the work in 10 days. In how many days can B alone do the work? .

In one day A and B together can do of the work.

A alone can do th of the work

So B can do of the work in one day.

So B can do the work in 60 days.

A and B can do a work in 12 days and 20 days respectively. A started the work and left after 3 days. B immediately took over and worked till the completion. In how many days was the total work completed? .

A can do of work in one day. So he can do x 3 = th of the work in 3 days. After 3 days of the work is still left over.

B can do th of the work in one day. So he can do of work in = 15 days

So total time taken is 15 + 3 = 18 days. .

A and B can complete a work in 6 days, B and C in 8 days and A and C in 10 days. If all three work together, in how many days will the work will be completed? .

One day work of,

A and B =

B and C =

A and C =

two days of work (A + B + C)

=

one day of work (A + B + C) =

So, they can complete the work in days i.e., days

A can do a work in 6 days more than what B takes to do the work. A worked for 7 days, then B takes the work and completed it in 10 more days. In how many days each of them can complete the work individually? .

Let B take x days to do the work. .

A takes (x + 6) days to do the work. .

Work done by A in 7 days =

Work done by B in 10 days =

So = 1

= 1

17x + 60 = x^{2} + 6x

&⇒ x^{2} - 11x - 60 = 0

&⇒ x^{2} - 15x + 4x - 60 =
0

&⇒ x (x - 15) + 4 (x - 15) = 0

&⇒ x = 15

A can do the work in 21 days and B can do it in 15 days.