Time and work questions

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Time And Work

Question 46 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A group of men decided to do a job in 4 days. But since 20 men dropped out every day, the job completed at the end of the 7th day. How many men were there at the beginning?
A
150
B
140
C
240
D
280
Question 46 Explanation: 
Let X be the initial number of men then,

According to the question,

4X = X + (X-20) + (X-40) + (X-60) + (X-80) + (X-100) + (X-120)

==> 4X = 7X-420

==> 3X = 420

==> X = 420/3

==> X = 140 men.

Question 47 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
A
6 5/11
B
5 6/11
C
6 6/11
D
5 5/11
Question 47 Explanation: 
\begin{align} & {\text{P}}\, {\text{can}}\, {\text{complete}}\, {\text{the}}\, {\text{work}} \cr & = \, \left( {12 \times 8} \right){\text{hrs}}{\text{.}} = 96\, {\text{hrs}}{\text{.}} \cr & {\text{Q}}\, {\text{can}}\, {\text{complete}}\, {\text{the}}\, {\text{work}} \cr & = \left( {8 \times 10} \right){\text{hrs}}{\text{.}} = 80\, {\text{hrs}}{\text{.}} \cr & \therefore {\text{P's}}\, {\text{1}}\, {\text{hour's}}\, {\text{work}} = \frac{1}{{96}}\, {\text{and}} \cr & \therefore {\text{Q's}}\, {\text{1}}\, {\text{hour's}}\, {\text{work}} = \frac{1}{{80}} \cr & \left( {{\text{P + Q}}} \right){\text{'s}}\, {\text{1}}\, {\text{hour's}}\, {\text{work}} \cr & = \left( {\frac{1}{{96}} + \frac{1}{{80}}} \right) = \frac{{11}}{{480}} \cr & {\text{So, }}\, {\text{both}}\, {\text{P}}\, {\text{and}}\, {\text{Q}}\, {\text{will}}\, {\text{finish}}\, {\text{the}}\, {\text{work}} \cr & = \left( {\frac{{480}}{{11}}} \right){\text{hrs}}{\text{.}} \cr & \therefore {\text{Number}}\, {\text{of}}\, {\text{days}}\, {\text{of}}\, {\text{8}}\, {\text{hours}}\, {\text{each}} \cr & \left( {\frac{{480}}{{11}} \times \frac{1}{8}} \right) = \frac{{60}}{{11}}{\text{days}} = 5\frac{5}{{11}}{\text{days}} \cr\end{align}
Question 48 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A is thrice good a workman as B and therefore is able to finish a job in 40 days less than B. Working together they can do it in:
A
15 days
B
18 days
C
16 days
D
20 days
Question 48 Explanation: 
Given,

A is thrice good work man as B. Means,

A = 3B

Let B can finish work in X days, then A will finish same work in (X-40) days alone.

Now,

BX = 3B*(X-40)

X = 60 days.

B can finish work in 60 days, then A can finish the work in 20 days.

One day work of B = 1/60

One day work of A = 1/20

One day work of (A+B) = (1/60)+(1/20) = (1+3)/60 = 1/15.

So, they can finish work together in 15 days.

Question 49 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?
A
12:30 P.M.
B
1:00 P.M.
C
12 noon
D
11:30 A.M.
Question 49 Explanation: 
\begin{align} & \left( {{\text{P + Q + R}}} \right){\text{'s}}\, {\text{1}}\, {\text{hour's}}\, {\text{work}} \cr & = \left( {\frac{1}{8} + \frac{1}{{10}} + \frac{1}{{12}}} \right) = \frac{{37}}{{120}} \cr & {\text{Work}}\, {\text{done}}\, {\text{by}}\, {\text{P, }}\, {\text{Q}}\, {\text{and}}\, {\text{R}}\, {\text{in}}\, {\text{2}}\, {\text{hours}} \cr & = \left( {\frac{{37}}{{120}} \times 2} \right) = \frac{{37}}{{60}} \cr & {\text{Remaining}}\, {\text{work}} = \left( {1 - \frac{{37}}{{60}}} \right) = \frac{{23}}{{60}} \cr & \left( {{\text{Q + R}}} \right){\text{'s}}\, {\text{1}}\, {\text{hour's}}\, {\text{work}} \cr & = \left( {\frac{1}{{10}} + \frac{1}{{12}}} \right) = \frac{{11}}{{60}} \cr & {\text{Now}}, \frac{{11}}{{60}}\, {\text{work}}\, {\text{is}}\, {\text{done}}\, {\text{by}}\, {\text{Q}}\, \, {\text{and}}\, {\text{R}}\, {\text{in}}\, {\text{1}}\, {\text{hour}} \cr & {\text{So}}, \frac{{23}}{{60}}\, {\text{work}}\, {\text{will}}\, {\text{be}}\, {\text{done}}\, {\text{by}}\, {\text{Q}}\, {\text{and}}\, {\text{R}}\, {\text{in}} \cr & \left( {\frac{{60}}{{11}} \times \frac{{23}}{{60}}} \right) = \frac{{23}}{{11}}\, {\text{hours}} \approx 2\, {\text{hours}} \cr & {\text{So, }}{\text{the}}\, {\text{work}}\, {\text{will}}\, {\text{be}}\, {\text{finished}}\, {\text{approximately}} \cr & {\text{2}}\, {\text{hours}}\, {\text{after}}\, {\text{11}}\, {\text{A}}{\text{.M}}{\text{., }}\, {\text{i}}{\text{.e}}{\text{., }}\, {\text{around}}\, {\text{1}}\, {\text{P}}{\text{.M}}{\text{.}} \cr\end{align}
Question 50 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
A
20 3/17
B
13 days
C
11 days
D
None of these
Question 50 Explanation: 
\begin{align} & {\text{Ratio}}\, {\text{of}}\, {\text{times}}\, {\text{taken}}\, {\text{by}}\, {\text{A}}\, {\text{and}}\, {\text{B}} \cr & = 100:130 = 10:13 \cr & {\text{Suppose}}\, {\text{B}}\, {\text{takes}}\, x\, {\text{days}}\, {\text{to}}\, {\text{do}}\, {\text{the}}\, {\text{work}} \cr & {\text{Then}}, 10:13::23:x \cr & \Rightarrow x = \left( {\frac{{23 \times 13}}{{10}}} \right) \cr & \Rightarrow x = \frac{{299}}{{10}} \cr & {\text{A's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{1}{{23}} \cr & {\text{B's}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{{10}}{{299}} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {\frac{1}{{23}} + \frac{{10}}{{299}}} \right) \cr & = \frac{{23}}{{299}} \cr & = \frac{1}{{13}} \cr & \therefore A\, {\text{and}}\, {\text{B}}\, {\text{together}}\, {\text{can}}\, {\text{complete}} \cr & \, {\text{the}}\, {\text{work}}\, {\text{in}}\, {\text{13}}\, {\text{days}}{\text{.}} \cr\end{align}
There are 50 questions to complete.

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