Latest CAT Aptitude Question SOLUTION: Three pipes a b and c can fill a tank in 6hrs. after working at it together for 2 hrs c is closed and a and b can fill the remaining part in 7hrs. The number of hours taken by c a

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(#M40034680) CAT Numerical Ability question pipes and cisterns Keep an EYE

Three pipes a b and c can fill a tank in 6hrs. after working at it together for 2 hrs c is closed and a and b can fill the remaining part in 7hrs. The number of hours taken by c alone to fill the tank is

Asked In CAT ramakrishna (10 years ago)

Solved Ann Theressa Read Solution (7)

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Read Solution (7) :

Ann Theressa  (10 years ago)

14 hours

Let a and be take x hours to fill the tank
and c take y hours to fill the tank

Together they can fill in 6 hours
1/x + 1/y = 1/6 ---(1)

===> in 1 hour = 1/6 is filled
in 2 hours = 1/6*2 = 1/3 filled

Remaining fraction to be filled = 2/3

a and b takes 7 hours to fill 2/3 part
7 hours --- 2/3 part
x hours ---- 1 part

x = 7*3/2 = 21/2 hours

put x =21/2 in equation (1)

2/21 + 1/y = 1/6
1/y = 1/14
===> y= 14 hours

c alone takes 14 hours to fill the tank

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Saraswathy  (10 years ago)

sorry its 14 hrs

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Saraswathy  (10 years ago)

a + b + c's 1 hr work = 1/6
a+b + c 's 2 hr work = 2 * 1/6 = 1/3

Remaining work = 1 - 1/3 = 2/3

a+b ll fill 2/3 part of tank in 7 hrs
a+b ll fill d full tank in 3/2 * 7 = 21/2

Part of d tank filled by c in 1 hr = (a+b+c)'s 1hr work - (a+b)'s 1 hr work
===> 1/6 - 2/21 = 9/126 = 3/42 = 1/14

C ll fill d full tank in 42hrs

Ans : 42hrs

Is this solution Helpfull? Yes (1) | No (3)  

Vivek  (10 years ago)

a+b+c do in 1hr=1/6..........................................(i)
a+b+c do in 2hrs=1/6*2=1/3
Remaining=1-1/3=2/3

a+b do 2/3 part in 7 hrs.
a+b do 1 part full in 21/2 hrs.

a+b do in 1hr= 2/21.........................................(ii)

By doing, (i)-(ii), we get-

c=1/14.
So, c does the full work alone in 14hrs.

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sravani  (9 years ago)

a + b + c=1/6
for 2hrs work completed is 2(a+b+c)=2(1/6)=1/3
so, work remaining=1-1/3=2/3
2/3work done by a+b in7hrs..
whole work by a+b=2/3*7= 2/21
therefore,(a+b+c) - (a+b) =1/6 - 2/21 = 1/14
so, c takes 14 days to complete whole work...

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shashank raj  (10 years ago)

A+b+c=6hr; means 100/6=16.66% of work in in hr
So 2hr work is 2×16.66=33.32%
Remaining work is 66.68%
A+b fill the remaining part 66.68/7=9.52%
So 1 hr work of c=(a+b+c)-(a+b).......1hr work
I.e approx 5.14% and will be 100/5.14 ...
So approx near to 19hr ....

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SUCHETAN SASIS  (10 years ago)

4.5
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