**Type 7 – Partial work**

**1. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?**

**Solution:**

Amount of
work P can do in 1 day = 1/20

Amount of
work Q can do in 1 day = 1/30

Amount of
work R can do in 1 day = 1/60

P is
working alone and every third day Q and R is helping him

Work
completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work
completed in 15 days = 5 × 1/5 = 1

i.e, the
work will be done in 15 days

**2. There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?**

**Solution:**

Work
completed in 1st day = 1/16

Work
completed in 2nd day = (1/16) + (1/16) = 2/16

Work
completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16

An easy way
to attack such problems is from the choices. You can see the choices are very
close to each other. So just see one by one.

For
instance, The first choice given in 3 1⁄4

The work
done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16

The work
done in 4 days = (1+2+3+4)/16 = 10/16

The work
done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?

The work
done in 6 days = (1+2+3+4+5+6)/16 > 1

Hence the
answer is less than 6, but greater than 5. Hence the answer is 5 1⁄6 days.

**3. Pintu, Bittu and Bonku undertake to do a work for Rs.6400. Pintu and Bittu worked together to finish 25% of the work. Bonku then took up the work and finished the rest of it alone. How much will Bonku get?**

**Solution:**

Pintu and
Bittu finished 25% of the work and so received 25% of the contracted amount of
money, which is

Rs.1600. As
Bonku finished the rest of the work alone, he must take away rest of the
contracted amount, that is,

Rs.6400 –
Rs.1600 = Rs.4800

**4. Ashish can do 400% of a work in 24 days while Srinath can do 50% of the same work in 2 days. Find the time required to complete 200% of the work, if both are working together.**

**Solution:**

Ashish →
400% → 24 days

Ashish →
100% (or 1 work) → 6 days

Ashish →
200% → 12 days

Srinath →
50% → 2 days

Srinath →
100% → 4 days

Srinath →
200% → 8 days

(1 / 12) +
(1 / 8) = 5 / 24

Hence, no.
of days = 24 / 5 = 4(4 / 5) days

**Type 8 – Alternating work**

**1. A & B working alone can do a work in 9 and 12 days respectively. If they work for a day alternately, A beginning, in how many days the work will be completed?**

**Solution:**

Let's take
the least common multiple for these 2work rates - The LCM is 36.

Assume they
have to create 36 items each.

A can
complete 4 in a day (36/9)

B can
complete 3 in a day (36/12)

Since the
sequence starts with A, they can complete 35 items in 10 days
(4+3+4+3+4+3+4+3+4+3).

Since it's
A's turn next, he can complete 1 item in 1/4 day

Therefore,
total- 10+1/4 = 41/4

**2. A alone can complete a work in 16 days and B alone can do in 12 days. Starting with A, they work on alternate days. The total work will be completed in**

**Solution:**

A's 1 day
work = 1/16

B's 1 day
work = 1/12

As they are
working on alternate days

So their 2
days work = (1/16) + (1/12) = 7/48

[here is a
small technique, Total work done will be 1, right, then multiply numerator till
denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider
7*6, means 6 pairs ]

Work done
in 6 pairs = 6*(7/48) = 7/8

Remaining
work = 1-7/8 = 1/8

On 13th day
it will A turn, Then remaining work = (1/8)-(1/16) = 1/16

On 14th day
it is B turn, 1/12 work done by B in 1 day

1/16 work
will be done in (12*1/16) = 3/4 day

So total
days = 13 ¾

**Type 9 – Chain rule**

**1. Fifty six men can complete a piece work in 24 days. In how many days can 42 men complete the same piece of work?**

**Solution:**

56 men can
complete 1 work in 24 days.

∴ 1 men
complete the work in 24 × 56 days.

∴ 42 men
will do the same work in 24 * 56 / 42 = 32 days

Alternative
method: ∴ M1D1 =
M2D2

∴ 56 × 24 =
42 × D2

=> D2 =
56 * 24 / 42 = 32 days.

**2. 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.**

**Solution:**

Let work
done by 1 man in 1 day = m and work done by 1 woman in 1 day = b

Work done
by 6 men and 8 women in 1 day = 1/10

=> 6m +
8b = 1/10

=> 60m +
80b = 1 --- (1)

Work done
by 26 men and 48 women in 1 day = 1/2

=> 26m +
48b = ½ => 52m + 96b = 1--- (2)

Solving
equation 1 and equation 2, We get m = 1/100 and b = 1/200

Work done
by 15 men and 20 women in 1 day

= 15/100 +
20/200 =1/4

=> Time
taken by 15 men and 20 women in doing the work = 4 days