# Quantitative Aptitude Notes: Time and Work (Part - 3)

Quantitative Aptitude Notes: Time and Work (Part – 3)
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