1. 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
|
B alone
will take 12 hours to do the work.
2. B's 10 day's work =
|
1
/ |
x 10
|
=
|
2
/ |
.
|
||
15
|
3
|
Remaining work =
|
1 -
|
2
/ |
=
|
1
/ |
.
|
||
3
|
3
|
Now,
|
1
/ |
work is done by A in 1 day.
|
18
|
1
/ |
work is done by A in
|
18 x
|
1
/ |
= 6 days.
|
|||
3
|
3
|
||||||
3. 1
woman's 1 day's work =
|
1
/ |
70
|
1 child's 1 day's work =
|
1
/ |
140
|
(5 women + 10 children)'s day's work =
|
5
/ |
+
|
10
/ |
=
|
1
/ |
+
|
1
/ |
=
|
1
/ |
||||
70
|
140
|
14
|
14
|
7
|
5 women
and 10 children will complete the work in 7 days.
4 .Number of pages typed by Ravi in 1 hour =
|
32
/ |
=
|
16
/ |
. |
6
|
3
|
Number of pages typed by Kumar in 1 hour =
|
40
/ |
= 8.
|
5
|
Number of pages typed by both in 1 hour =
|
16
/ |
+ 8
|
=
|
40
/ |
.
|
||
3
|
3
|
Time
taken by both to type 110 pages =
|
110 x
|
3
/ |
hours
|
||
40
|
= 8
|
1
/ |
hours (or) 8 hours 15 minutes.
|
4
|
5. Ratio of times taken by Sakshi and
Tanya = 125 : 100 = 5 : 4.
Suppose Tanya takes x days to do the work.
5 : 4 :: 20
: x x =
|
4 x 20
/ |
||
5
|
x =
16 days.
Hence, Tanya takes 16 days to complete the work.
6. Suppose A, B and C take x,
|
x
/ |
and
|
x
/ |
days respectively to finish the work.
|
2
|
3
|
Then,
|
1
/ |
+
|
2
/ |
+
|
3
/ |
=
|
1
/ |
||
x
|
x
|
x
|
2
|
6
/ |
=
|
1
/ |
|
x
|
2
|
x =
12.
So, B takes (12/2) = 6 days to finish the work.
7. (A + B
+ C)'s 1 day's work =
|
1
/ |
,
|
4
|
A's 1 day's work =
|
1
/ |
,
|
16
|
B's 1 day's work =
|
1
/ |
.
|
12
|
C's
1 day's work =
|
1
/ |
-
|
1
/ |
+
|
1
/ |
=
|
1
/ |
-
|
7
/ |
=
|
5
/ |
.
|
||||
4
|
16
|
12
|
4
|
48
|
48
|
So,
C alone can do the work in
|
48
/ |
= 9
|
3
/ |
days.
|
5
|
5
|
8. (A+B)'s 1 day work = 1/4
A's 1 day work = 1/12
B's 1 day work = (1/4−1/12) = 3− 1/12 = 1/6
So B alone can complete the work in 6 days
9. Firstly we will find 1 day work of both A
and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/10
B's 1 day work = 1/15
(A+B)'s 1 day work = (1/10+1/15)=(3+2/30)=1/6
So together they can complete work in 6 days.
So,
A's 1 day work = 1/10
B's 1 day work = 1/15
(A+B)'s 1 day work = (1/10+1/15)=(3+2/30)=1/6
So together they can complete work in 6 days.
10. Let's take the least common
multiple for these 2work rates - The LCM is 36.
Assume they have to create 36 items each.
A can complete 4 in a day (36/9)
B can complete 3 in a day (36/12)
Since the sequence starts with A, they can complete 35 items in 10 days
(4+3+4+3+4+3+4+3+4+3). Since it's A's turn next, he can complete 1 item in 1/4 day
therefore total- 10+1/4 = 41/4
Assume they have to create 36 items each.
A can complete 4 in a day (36/9)
B can complete 3 in a day (36/12)
Since the sequence starts with A, they can complete 35 items in 10 days
(4+3+4+3+4+3+4+3+4+3). Since it's A's turn next, he can complete 1 item in 1/4 day
therefore total- 10+1/4 = 41/4
11. A's 1 day work = 1/16
B's 1 day work = 1/12
As they are working on alternate day's
So their 2 days work = (1/16)+(1/12)
= 7/48
[here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]
Work done in 6 pairs = 6*(7/48) = 7/8
Remaining work = 1-7/8 = 1/8
On 13th day it will A turn,
then remaining work = (1/8)-(1/16) = 1/16
On 14th day it is B turn,
1/12 work done by B in 1 day
1/16 work will be done in (12*1/16) = 3/4 day
So total days = 13 ¾
B's 1 day work = 1/12
As they are working on alternate day's
So their 2 days work = (1/16)+(1/12)
= 7/48
[here is a small technique, Total work done will be 1, right, then multiply numerator till denominator, as 7*6 = 42, 7*7 = 49, as 7*7 is more than 48, so we will consider 7*6, means 6 pairs ]
Work done in 6 pairs = 6*(7/48) = 7/8
Remaining work = 1-7/8 = 1/8
On 13th day it will A turn,
then remaining work = (1/8)-(1/16) = 1/16
On 14th day it is B turn,
1/12 work done by B in 1 day
1/16 work will be done in (12*1/16) = 3/4 day
So total days = 13 ¾
12. Work done by the waste pipe in 1 minute
=
1/15-[1/20+1/24]
|
=1/15-11/120
=-1/40
= volume of 1/40 part= 3 gallons.
Therefore, Volume of whole =(3×40)gallons = 120 gallons
13. Let the
tap completely fill the tank (with no hole in it) in x min
⇒ 1/x-1/4= 1/x+2
⇒ x= 2 minutes.
14. Red light flashes
every 20 seconds
Green light flashes every 24 seconds Therefore, they will flash together every 120 seconds In every hour they will flash
= 30 times
15. Ram takes 24 days to complete the work,
if he works alone.
As Krish is twice as efficient as Ram is, Krish will take half the time to complete the work when Krish works alone, i.e., in 12 days. Ram completes (1/24) th of the work in a day.
Krish completes (1/12 ) th of the work in a day.
When they work together, they will complete
=
1/8 work in a day.
Therefore, when they work together they will complete the
work in 8 days.
|
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