Time and work

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6. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
A. 4 days B. 5 days
C. 6 days D. 7 days

Answer: Option A

Explanation:

 

Let 1 man’s 1 day’s work = x and 1 boy’s 1 day’s work = y.

 

Then, 6x + 8y = 1 and 26x + 48y = 1 .
10 2

 

Solving these two equations, we get : x = 1 and y = 1 .
100 200

 

(15 men + 20 boy)’s 1 day’s work = 15 + 20 = 1 .
100 200 4

15 men and 20 boys can do the work in 4 days.
7. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A. 8 hours B. 10 hours
C. 12 hours D. 24 hours

Answer: Option C

Explanation:

 

 

A’s 1 hour’s work = 1 ;
4

 

(B + C)’s 1 hour’s work = 1 ;
3

 

(A + C)’s 1 hour’s work = 1 .
2

 

(A + B + C)’s 1 hour’s work = ( 1 + 1 ) = 7 .
4 3 12

 

B’s 1 hour’s work = ( 7 – 1 ) = 1 .
12 2 12

Therefore B alone will take 12 hours to do the work.
8. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
A. 15 days B. 20 days
C. 25 days D. 30 days

Answer: Option C

Explanation:

 

 

(A + B)’s 1 day’s work = 1
10

 

C’s 1 day’s work = 1
50

 

(A + B + C)’s 1 day’s work = 1 + 1 = 6 = 3 . …. (i)
10 50 50 25

A’s 1 day’s work = (B + C)’s 1 day’s work …. (ii)

 

From (i) and (ii), we get: 2 x (A’s 1 day’s work) = 3
25

 

A’s 1 day’s work = 3 .
50

 

B’s 1 day’s work 1 – 3 = 2 = 1 .
10 50 50 25

So, B alone could do the work in 25 days.
9. A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
A. 23 days B. 37 days
C. 371/2 D. 40 days

Answer: Option C

Explanation:

 

 

Whole work is done by A in ( 20 x 5 ) = 25 days.
4

 

Now, ( 1 – 4 ) i.e., 1 work is done by A and B in 3 days.
5 5

Whole work will be done by A and B in (3 x 5) = 15 days.

 

A’s 1 day’s work = 1 , (A + B)’s 1 day’s work = 1 .
25 15

 

Therefore B’s 1 day’s work = ( 1 – 1 ) = 4 = 2 .
15 25 150 75

 

So, B alone would do the work in 75 = 37 1 days.
2 2
10. 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. 11:30 A.M. B. 12 noon
C. 12:30 P.M. D. 1:00 P.M.

Answer: Option D

Explanation:

 

 

(P + Q + R)’s 1 hour’s work = ( 1 + 1 + 1 ) = 37 .
8 10 12 120

 

Work done by P, Q and R in 2 hours = ( 37 x 2 ) = 37 .
120 60

 

Remaining work = ( 1 – 37 ) = 23 .
60 60

 

(Q + R)’s 1 hour’s work = ( 1 + 1 ) = 11 .
10 12 60

 

Now, 11 work is done by Q and R in 1 hour.
60

 

So, 23 work will be done by Q and R in ( 60 x 23 ) = 23 hours = 2 hours.
60 11 60 11

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.
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