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127. 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
✅ The correct answer is option C.
(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.

129. 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.
✅ The correct answer is option D.
(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.

131. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :

[A]. 4 days
[B]. 6 days
[C]. 8 days
[D]. 18 days
✅ The correct answer is option A.
Ratio of rates of working of A and B = 2 : 1.
So, ratio of times taken = 1 : 2.

B’s 1 day’s work =
1
.

12

A’s 1 day’s work =
1
; (2 times of B’s work)

6

(A + B)’s 1 day’s work =

1
+
1

=
3
=
1
.

6
12
12
4

So, A and B together can finish the work in 4 days.

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