Mission CGL Mains 2015 : Tricks and Quiz on Time and Work

Dear Readers,
In continuance to the “MISSION CGL MAINS 2015”, we are providing you a Short tricks  and a quiz on Time and Work  in Quant Section.that can be helpful for  all the SSC Mains exam, SSC aspirants exam including FCI Exam.

Important facts:
(a)  If A can do a piece of work in n days, then A’s 1 day’s work = 1/n
(b)  If A’s 1 day’s work = 1/n, then A can finish the work in n days.
(c)  If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3:1
Ratio of times taken by A and B to finish a work= 1:3

then the general formula in the relationship of
M1 D1 W2 = M2 D2 W1
1.More men less days and conversely more days less men.
2.More men more work and conversely more work men.
3.More days more work and conversely more work days.

Work & Wages
Wages are distributed in proportion to the work done and in indirect (or inverse) proportion to the time taken by the individual. 
There are two methods: – 
Eg. A can do a work in 3 days and B can do the same work in 5 days. The contract for the work is Rs. 240. How much shall B get If both of them work together. 
Methods I : – 
A’s 1 day’s work = 1/3; B’s 1 days work = 1/5  
Ratio of their wages = 1/3:1/5=5∶3
B’s share = 240/(5+3)  ×3 = Rs. 90 
Methods II : – 
As wages are distributed in inverse proportion of number of days, their share should be in the ratio 5 : 3 
B’s share =   240/8  ×3 = Rs. 90
Some Questions based on above Concept:
1.A and B can do a work in 7(1/2 )days and 30 days respectively. In how many days can they complete the  work if they work together?
(a) 5
(b) 4
(c) 6
(d) 3
2.A can do a work in 24 days. B and C together can do the same work in 18 days. In how many days can A, B and C together do a work which is 3(1/2) times the previous work?
(a) 32 days
(b) 28 days
(c) 36 days
(d) 40 days
3.A, B and C together can do a work in 22 days. B and C can do 3/4 of work in 30 days. In how many days can A alone do the work?
(a) 47(8/9)
(b) 48(7/9)
(c) 48(8/9)
(d) 47(7/9)
4.A and B working together can complete a work in 6 days. A alone can complete the same work in 10 days. Every day if B works only half a day then in how many days can A and B together complete the work?
(a) 12 days
(b) 8 days
(c) 7(1/2) days
(d) 4(1/2) days
5.A can do half as much work as B in two – fifth of the time taken by B. If together they take 20 days, how much time shall B take to do it alone?
(a) 15 days
(b) 90 days
(c) 45 days
(d) 60 days
6.A is 80% as efficient as B. C does two-third of the work done by A and B together in the same time. If C alone does the work in 10 days. Then A and C, together can do the work in__________.
(a) 12 days
(b) 24 days
(c) 18 days
(d) 6 days
7.One man and one woman together can complete a piece of work in 18 days. A man alone can complete the work in 30 days. In how many days can one woman alone complete the work?
(a) 45 days
(b) 54 days
(c) 60 days
(d) 72 days
8.A can do a work in 21 days and B in 28 days. Together they started the work and B left after 4 days. In how many days can A alone do the remaining work?
(a) 12
(b) 10
(c) 16
(d) 14
9.22 skilled men can do a piece of work in 10 days and 45 unskilled men can do the work in 30 days. In how many days can 45 unskilled and 22 skilled men do the work?
(a) 10
(b) 9
(c) 8.5
(d) 7.5
10.24 men can prepare 12 toys in 6 days working 6 hrs a day then in how many days can 18 men prepare 15 toys working 6 hours a day?
(a) 10
(b) 13
(c) 12
(d) 15

Answers and Solution:
1.(c)
Part of the work done by A and B in one day
= 2/15 + 1/30 = 1/6
so ,A and B together can do the work in 6 days.

2.(c)
A,B and C in one day can do 1/24 + 1/18 = 7/72 of the work.
A,B and C together can do the work in 72/7 days.
So,they can do 3(1/2) times the work in 72/7*7/2 = 36  days
3.(c) 
B and C can do the work in 30 *4/3 = 40 days.
A’s one day work = 1/22 – 1/40 = 9/440
A can do the work in 440/9 = 48(8/9) days
4.(c)
5.(c)
Let B alone can do the work in ‘X’ days
=> A alone can do the work in (2x/5)/(1/2) = 4x/5 days
=> 1/x + 1/(4x/5) = 1/20
x = 45

6.(d)
7.(a)
Let the part of the work done by a man and a woman in one day be m and w respectively.
Given : m + w = 1/18
And m = 1/30
so w = 1/18 – 1/30 = 1/45
=> A woman alone can complete the work in 45 days.
8.(d)
9.(d)
One day work of 45 unskilled and 22 skilled workers = 1/30 + 1/10 = 2/15
So they take = 15/2 = 7.5 days

10.(a)
M1D1H1W2 = M2D2H2W1
24*6*6*15 = 18*6*12*D
D = 10 days.


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