Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is cl

M4maths Previous Puzzles

03 Dec 2014 Time and Word

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill it in 7 hours. The number of hours taken by C alone to fill the cistern, is:

OPtion

1) 10
2) 21
3) 12
4) 22
5) 14
6) 20
7) 16
8) 15
9) 18
10)None of these

Solution

Part filled in 2 hours = 2/6 = 1/3. Remaining part = 2/3
(A + B)'s 7 hours' work = 2/3.
So, (A+B)'s 1 hr work = 2/21
Therefore C's 1 hour's work
= [(A+B+C)'s 1 hour]-[(A+B)'s 1 hr work]
=(1/6 - 2/21) = 1/14
C alone can fill the tank in 14 hours

Option 5)

Correct Option: 5 Best Solution (34)

ITHA Naresh Babu   10 years AGO

suppose that the capacity of tank is 42 units(lcm of 6,7)
a,b,c can fill tank in 6 hours=>a,b,c can fill (42/6=)7 units per hour.---------->(1)
after 2 hours 14 units of tank is filled and 28 units is left.Given a,b takes 7 hours to fill the remaining tank(28 units)=>a,b fills 4 units of tank per hour.---------->(2)
From (1) &(2) we get that c fills 3 units of tank per hour.
Hence to fill the full(42 units) tank it takes (42/3=)14 hours

Like? Yes (65) | No (7)  

K.ARun   10 years AGO

Three Pipes A,B and C together filled a tank in 6 hours
so 1hr work of A,B and C is 1/6
2hr working together 2/6
rem part nedd to be filled is (1-2/6)
i.e 2/3

(A+B)'s 7hr work = 2/3
(A+B)'s 1hr work= 2/3*7--> 2/21

C's 1hr work= (A=B+C)'s 1hr work -(A+B)'s 1hr Work
so.. 1/6-2/21
by solving leads to the answer 1/14
so 14hrs :)

Like? Yes (24) | No (7)  

priyanka    10 years AGO

a,b,c one hour work = 6 hour
1 hour work =1/6
2 hour =1/3
left work 2/3 coverd in 7 hours by a nd b
c work 1/6-2/21=1/14
14 hour...

Like? Yes (9) | No (1)  

P.Pandeeswari   10 years AGO

1/a+1/b+1/c=1/6

after working for 2 hrs. the work done is 1/3. so the

remaining work is 2/3.

which is done by a and b in 21 /2 hrs.

1/a+1/b+1/c=1/6

1/a+1/b=2/21

so 1/c-1/6-2/21= 14 hrs.

ans is

option 5) 14

Like? Yes (15) | No (8)  

Vishal Chugh   10 years AGO

a+b+c=6
efficiency=1
a+b effi.12/21
c effi=9/21
6*21/9=14

Like? Yes (24) | No (18)  

Udhaya kumar   10 years AGO

6 (1/a + 1/b +1/c) = 1
2(1/a + 1/b +1/c) + 7(1/a + 1/b) = 1
let (1/a + 1/b) = x and 1/c as y
6x + 6y = 1
9x + 2y = 1
by solving y = 0.07142
c = 1/y = 14..........

Like? Yes (8) | No (3)  

lakshmi   10 years AGO

Part filled in 2 hours = 2/6 = 1/3

Remaining part = (1-1/3) = 2/3 .

(A + B)'s 7 hour's work =2/3

(A + B)'s 1 hour's work =2/21

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

=1/6 - 2/21 =1/14

C alone can fill the tank in 14 hours.

Like? Yes (6) | No (4)  

Sanu Panji   10 years AGO

A+B+C do whole work in 6 hrs.

A+B+C works in 2 hr 2/6= 1/3 fraction of whole work
rest (1-1/3)= 2/3 fraction A+B do in 7 hr

so, A+B do whole work in 7/(2/3)=7*3//2=10.5 hrs

so, C does whole work in (10.5*6)/(10.5-6)= 14 hrs

Correct option is (5)

Like? Yes (3) | No (1)  

Chirag Ranjan Lahiri   10 years AGO

Part filled in 2 hours = 1/3
Remaining = 2/3
(A + B)'s 7 hour's work = 2/3
(A + B)'s 1 hour's work = 2/21
So, C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work } = 1/6 - 2/21 = 1/14

Hence, C alone can fill the tank in 14 hours.

Like? Yes (5) | No (3)  

Surit Datta   10 years AGO

Part filled in 2 hours = 2/6 = 1/3
Remaining part = ( 1 - 1/3) = 2/3
(A + B)'s 7 hour's work = 2/3
(A + B)'s 1 hour's work = 2/21
C's 1 hour's work =
{ (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }
(1/6 - 2/21) = 1/14
C alone can fill the tank in 14 hours.
That's it.

Like? Yes (5) | No (3)  

A.P.Singh   10 years AGO

Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed ( After filling 1/3 tank) and A and B can fill ( balance 2/3 tank ) it in 7 hours. A & B can fill full tank in 7*3/2=21/2 hrs.
A&B can fill 2/21 tank in 1 hr.
C can fill 1/6 -2/21 = 3/42 or 1/14 tank in 1 hr.

so
The number of hours taken by C alone to fill the cistern, is 14

Like? Yes (4) | No (2)  

Ashwin Dinesh   10 years AGO

Let A, B, C can fill a, b, c part of the tank in 6 hrs.
1/a + 1/b + 1/c = 1/6
In 2 hrs: 2(1/a + 1/b + 1/c) = 1/3
A and B can fill the tank in 7 hrs after this...
7(1/a + 1/b) = 7(1/6 - c) = 2/3
Solving the above equation, we get c= 1/14
So pipe C can fill the tank in 14 hrs alone.
Which is option 5)

Like? Yes (6) | No (4)  

Shreya Banerjee   10 years AGO

Part filled in 2 hours = 2/6 = 1/3

Remaining part = (1 - 1/3) = 2/3

Therefore (A + B)'s 7 hour's work = 2/3

(A + B)'s 1 hour's work = 2/21

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

= 1/6 - 2/21 = 1/14

Thus, C alone can fill the tank in 14 hours.

Like? Yes (5) | No (3)  

Abhishek singh   10 years AGO

as all can fill in 1 hr=1/6
c closed after 2 hr so total tank filled =1/3
left=2/3
a n b can fill remaining in 7 hr so i.e 2/3 so fully they can fill in 10.5 hr
so 1/10.5+1/c=1/6
solving we get c can fill in 14 hr.

Like? Yes (4) | No (2)  

Sundar Kumar   10 years AGO

Part filled in 2 hours = 2 /6 = 1/3

Remaining part = (1 - 1/3) = 2 /3 .

(A + B)'s 7 hour's work = 2/3

(A + B)'s 1 hour's work = 2/21

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

= (1 /6- 2 /21) = 1/14

C alone can fill the tank in 14 hours.
Answer: Option 5) 14

Like? Yes (3) | No (2)  

Devendra Marghade   10 years AGO

(A+B+C)'s 1 hr. filling= 1/6,
In 2 hrs. (A+B+C) will fill 2/6=1/3, & Remaining=2/3
For (A+B) it takes 7 hrs. to fill 2/3
So in 1 hr. (A+B) will fill (2/3)/7=2/21
1 hr. filling of C= 1 hr. filling of[ (A+B+C) - (A+B)]
=(1/6) -(2/21)=3/42=1/14
So 'C' alone can fill the cistern in 14 hours

Like? Yes (3) | No (2)  

Azhar Syed   10 years AGO

1/A+1/B+1/C=1/6
working for 2 hrs A,B,C can do 1/3rd of work and remaining work is done by A,B in 7 hrs if A,B does this total work together it takes 10.5 hrs.
hence work done by C alone is 1/6-1/10.5=1/14
there fore option 5 is correct it takes 14 hours

Like? Yes (3) | No (2)  

Manasa Kotha   10 years AGO

A+B+C 1 hours work is 1/6
in 2 hours they complete 1/3rd work and remaining 2/3rd work is completed by a and b in 7 hours so a+b one hour work is 2/21
so c's 1 hour work=1/6-2/21= 9/126=1/14
no of hour's taken by c alone is 14 hours

Like? Yes (2) | No (1)  

purushothama   10 years AGO

Part filled in 2 hours = 2/6 = 1/3

Remaining part = (1-1/3) = 2/3 .

(A + B)'s 7 hour's work =2/3

(A + B)'s 1 hour's work =2/21

C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }

=1/6 - 2/21 =1/14

C alone can fill the tank in 14 hours.

Like? Yes (2) | No (2)  

jayalakshmi   10 years AGO

1/a+1/b+1/c=1/6
after working for 2 hrs. the work done is 1/3. so the remaining work is 2/3.
which is done by a and b in 21 /2 hrs.
1/a+1/b+1/c=1/6
1/a+1/b=2/21
so 1/c-1/6-2/21= 14 hrs.

Like? Yes (2) | No (2)  

A M ANKIT KALLURAYA   10 years AGO

if a,b,c can do the work together in 6 days.....
(1/a+1/b+1/c)=1/6.............................1st eqn
if they work for two days then one third of the work will be done...
remaining two thirds of the work will be done by a and b in 7 days
so a and b will do the 2/21 work in 1 day
substituting this in the 1st equation we get c=14

Like? Yes (1) | No (1)  

ravi prakash   10 years AGO

let complete is x
then 2/3of x=7hours
x=21/2
now 1/a +1/b=2/21
so 1/c=1/6-2/21=1/14
c can fill in 14 hours

Like? Yes (1) | No (1)  

Rahul Rathod   10 years AGO

1/a+1/b+1/c=1/6
after working for 2 hrs. the work done is 1/3. so the remaining work is 2/3.
which is done by a and b in 21 /2 hrs.
1/a+1/b+1/c=1/6
1/a+1/b=2/21
so 1/c-1/6-2/21= 14 hrs.

Like? Yes (2) | No (3)  

Pramod Gaikwad   10 years AGO

1/a+1/b+1/c=1/6
remaining work 2/3 done by a and b in 21 /2 hrs.
1/a+1/b+1/c=1/6
1/a+1/b=2/21
so 1/c-1/6-2/21= 14 hrs.

Like? Yes (1) | No (2)  

bhagya   10 years AGO

Part filled in 2 hours = 2/6 = 1/3
Remaining part = 1 - 1/3 = 2/3
∴ (A + B)'s 7 hour's work = 2/3
⇒ (A + B)'s 1 hour's work = 2/21
∴ C's 1 hour's work = [(A + B +C)'s 1 hour's work - (A + B)'s 1 hour's work] = 1/6 - 2/21 = 1/14
∴ C alone can fill the tank in 14 hours.

Like? Yes (2) | No (3)  

CHANDA VIJAYALAKSHMI   10 years AGO

A+B+C = 1/6
For 2 hours = 2 (1/6) = 1/3
Remaining = 2/3
(A+B)’s 7 hours work = 2/3
(A+B)’s 1 hours work = 2/21
C’s 1 hour work = (A+B+C)’s work – (A+B)’s work
= 1/6 -2/21
= 9/126 = 1/14
C alone can fill the tank in 14 hours

Like? Yes (1) | No (2)  

nitesh gupta   10 years AGO

Part filled in 2 hours =1/3
Remaining =2/3
A+B 7 hour work = 2/3
A+B 1 hour work = 2/21
C one hour work = A+B+C one hour work - A+B one hour work
1/6-2/21=1/14

Like? Yes (2) | No (3)  

arun   10 years AGO

part filled in 2 hrs = 2/6 = 1/3
remaining work = (1-1/3) = 2/3

(A+B) do 2/3 work in 7hrs
1hr (A+B) do ,(1/A+1/B)= 2/21
so we hv 1/A + 1/B + 1/c = 1/6
2/21 + 1/C = 1/6
1/C = 1/6 - 2/21
1/C = 1/14
so C alone can complete in 14 hrs

Like? Yes (1) | No (2)  

Anubhav jain   10 years AGO

a+b+c=6 hour's
a+b =7 hours after c is closed
c alone a and b work completed in 14 hours

Like? Yes (6) | No (7)  

Anand Dwivedi   10 years AGO

total part filled in two hour:- 2/6=1/3

So reamaining= 1-1/2=2/3

so total A and B work in 7h= 2/3

So subtract C s Work -A+B work = 1/6-2/21=1/14

so total fill tank fill in 14 hour

Like? Yes (1) | No (3)  

Arul Shaijan   10 years AGO

A+B+C=1/6 part of tank per hour

i.e, in 2 hours, A+B+C=2/6 part of tank
so, 4/6 part of tank remaining
4/6 part filled in 7 hours by A+B
so, A+B=4/42=2/21 part of tank per hour

(A+B+C)-(A+B)=1/6-2/21.

hence C=1/14 = 14 hours

Like? Yes (1) | No (3)  

sanjeev kumar   10 years AGO

Ans 14

Like? Yes (1) | No (3)  

Mithun Kumar Kesari   10 years AGO

14 h

Like? Yes (4) | No (6)  

Manojkumar.K   10 years AGO

A+B(alone)=7hours
A,B,C each has 2 hours
c alone means=7*2=14 hours

Like? Yes (6) | No (12)