Time and work questions

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Time And Work

Question 56 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Subhash can copy 50 pages in 10 hours; Subhash and Prakash together can copy 300 pages in 40 hours. In how much time can Prakash copy 30 pages?
A
13 h
B
11 h
C
12 h
D
10 h
Question 56 Explanation: 
Number of page copied by (Subhash+ Prakash) in 1 hour = 300/40 = 7.5 pages;

Subhash copied pages in one hour = 50/10 = 5 pages

Hence, Prakash copied pages in one hour = 7.5-5 = 2.5;

Thus,

Prakash can copied 30 pages in = 30/2.5 = 12 hour.

Question 57 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A and B can compete a piece of work in 18 days. They worked together for 12 days and then A left. B alone finished the work in 15 days. If Rs. 1500 be paid for the work then A's share is:
A
Rs. 800
B
Rs. 600
C
Rs. 900
D
Rs. 750
Question 57 Explanation: 
A and B can complete the work in 18 days, work rate = 100/18 = 5.55% per day.

They together can complete the work in 12 days = 5.55 * 12 = 66.66%.

Now, A leaves and B takes another 15 days to complete the whole work, Work rate of B = 33.33/15 = 2.22% per day.

B work for (12+15) = 27 days.

So, Work done by B in 27 days = 2.22*27 = 60% And So 40% work is done by A. so there share should be 60% and 40% ratio.

A's share = 40% of 1500 = Rs. 600.

Question 58 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
A
12 days
B
6 days
C
8 days
D
4 days
Question 58 Explanation: 
\begin{align} & \left( {{\text{A + B + C}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{1}{6} \cr & \left( {{\text{A + B}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{1}{8} \cr & \left( {{\text{B + C}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} = \frac{1}{{12}} \cr & \therefore \left( {{\text{A + C}}} \right){\text{'s}}\, {\text{1}}\, {\text{day's}}\, {\text{work}} \cr & = \left( {2 \times \frac{1}{6}} \right) - \left( {\frac{1}{8} + \frac{1}{{12}}} \right) \cr & = \left( {\frac{1}{3} - \frac{5}{{24}}} \right) \cr & = \frac{3}{{24}} \cr & = \frac{1}{8} \cr & {\text{So, }}\, {\text{A}}\, {\text{and}}\, {\text{C}}\, {\text{together}}\, {\text{will}}\, {\text{do}}\, \cr & {\text{the}}\, {\text{work}}\, {\text{in}}\, {\text{8}}\, {\text{days}} \cr\end{align}
Question 59 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
While working 7 hour a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, 8 hour a day?
A
3 days
B
3.6 days
C
2.1 days
D
4 days
Question 59 Explanation: 
A can complete the work in 7*6 = 42 hours;

1 hour's work of A = 1/42;

B can complete the work in 7*8 = 56 hours;

1 hour's work of B = 1/56;

(A+B)'s 1 hour's work = 1/42 + 1/56 = 98/42 * 56;

(A+B) will take time to complete whole work,

working 7 hours a day = 42 * 56/98 = 24 hours;

Let X be the no. of days taken, working 8 hours a day to complete the work by A and B together.

Now, using work equivalence method ;

24 = 8 * X;

X = 24/8 = 3 days.

Question 60 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
A
8 hours 25 minutes
B
8 hours
C
8 hours 15 minutes
D
7 hours 30 minutes
Question 60 Explanation: 
\begin{align} & {\text{Number}}\, {\text{of}}\, {\text{pages}}\, {\text{typed}}\, {\text{by}}\, {\text{Ravi}}\, {\text{in}}\, {\text{1}}\, {\text{hour}} \cr & = \frac{{32}}{6} = \frac{{16}}{3} \cr & {\text{Number}}\, {\text{of}}\, {\text{pages}}\, {\text{typed}}\, {\text{by}}\, {\text{Kumar}}\, {\text{in}}\, {\text{1}}\, {\text{hour}} \cr & = \frac{{40}}{5} = 8 \cr & {\text{Number}}\, {\text{of}}\, {\text{pages}}\, {\text{typed}}\, {\text{by}}\, {\text{both}}\, {\text{in}}\, {\text{1}}\, {\text{hour}} \cr & = \left( {\frac{{16}}{3} + 8} \right) = \frac{{40}}{3} \cr & \therefore {\text{Time}}\, {\text{taken}}\, {\text{by}}\, {\text{both}}\, {\text{to}}\, {\text{type}}\, {\text{110}}\, {\text{pages}} \cr & = \left( {110 \times \frac{3}{{40}}} \right){\text{hours}} \cr & = 8\frac{1}{4}\, {\text{hours}}\, {\text{(or)}}\, {\text{8}}\, {\text{hours}}\, {\text{15}}\, {\text{minutes}} \cr\end{align}
There are 60 questions to complete.

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