M4maths Previous Puzzles

02 Jul 2015 Time and work

Three taps A, B & C are connected to a tank either to fill or empty the tank. All three together can fill the tank in 8 minute whereas only A & B can fill it in 12 min. In a particular day all the three taps are used to fill the tank, they all are opened for 4 min, then A is closed, remaining 2 works for next 2 min then B is closed. Finally C fill the tank in 1 min. In how much time B alone can fill the tank.

OPtion

1) 10 minute
2) 12 minute
3) 12 minute
4) 5 minute 15 second
5) 10 minute 30 second
6) 10 minute 40 second
7) 5 minute 20 second
8) 24 minute
9) 25 minute 50 second
10)18 minute

Solution

Let A, B & C fill the tank in x, y, z min respectively then according tot he given condition.
1/x + 1/y + 1/z = 1/8 (i)
1/x + 1/y = 1/12 (ii)
4/x + 6/y + 7/z = 1
On solving
y = 16/3 minute

Option 7)

Correct Option: 7 Best Solution (7)

Abhishek   9 years AGO

tank filled by C in 1 minute = 1/8 - 1/12 = 1/24 = 4.16%
In 4 minutes all of them filled the tank 50%.
now for next 2 minutes B & C works
i.e. B's 2 minute work + 8.33%
now C fills the tank in 1 minute = 4.16%
total 50% + B's 2 minute work + 12.50%=100%
B's 2 minute work =37.50%
B's one day work = 18.75%
So, B can do whole work in 100/18.75 = 5.33 minutes = 5 minute 20 second.

Like? Yes (7) | No (1)  

Vivek   9 years AGO

Let time taken by A to completely fill the tank be x min
Let time taken by B to completely fill the tank be y min
Let time taken by C to completely fill the tank be z min
Then Given
1/x +1/y +1/z =1/8
Also
1/x+1/y=1/12
Therefore 1/z=1/24
On that particular day
We have
4*(1/x+1/y+1/z)+2*(1/y+1/z)+1*1/z=1
4*1/8 +2*(1/y +1/24)+1/24=1
Simplifying this we get
y=16/3
=5 1/3 =5 min 20 sec
Therefore The answer is 7)

Like? Yes (5) | No   

Shiva Sharma   9 years AGO

Let speed of fluid is x1, x2,x3
let total quantity is Y
so:
12*x1+12*x2 = Y
8*x1+8*x2+8*x3 = Y
2*x2+3*x3 = Y/2
x3 = Y/24
x2 = 3*Y/16
so total time = 16/3 min = 5 min 20 sec

Like? Yes (3) | No   

vimal tiwari   9 years AGO

A+B+C=1/8 in 1 min
A+B= 1/12 in 1 min
so C will be 1/8 - 1/12 = 1/24

NOW all 3 works for 4 min so work after 4 min left
1 min = 1/8
4 min = 4*1/8 = 1/2

and C has to work for 1 min at last i.e. 7th min
and it can work 1/24 in 1 min so

definatly

1/2 - 2min work of B+c =1/24

so B+C = 11/48

B = 3/16 work in 1 min.
B can do full work in 16/3 min or 5min 20 sec

Like? Yes (3) | No   

Chandrima Goswami   9 years AGO

C alone can fill in 1 min= 1/8 - 1/12 = 1/24 part
B+C can fill in 2 min = 1- ( 1/2 + 1/24) = 11/24 part
and in 1 min = 11/48 part
B alone can fill in 1 min = 11/48 - 1/24 = 3/16 part
i.e B alone can fill the tank in 16/3 min = 5 min 20 sec
i.e Option 7)

Like? Yes (2) | No   

Nikhil chavan   9 years AGO

(1/x)+(1/y)+(1/z)=1/8
(1/x)+(1/y)=1/12
from here z=24
then solve 4(1/x+1/y+1/z)+2(1/y+1/z)+1/z=1
y=5 hours 20sec

Like? Yes (2) | No   

praveendas   9 years AGO

all togetherr fill in min is 1/8 ..for 4 miin half of the tank is filled..
c alone fill in min 1/8-1/12=1/24..
then from above cal we can find b is to take 48/9min to fill the tank

Like? Yes (1) | No