Two pipes, when working one at a time, can fill a cistern in 3 hhrs and 4 hrs, resp while a third pipe can drain the cistern empty in 8 hrs. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?

Correct Answer: 10

Correct Answer: 8 hours

Explanation:

Then 3/5 th tank fill in =40/3 * 3/5= 8 hours

Correct Answer: It empties in 4.8 min

Correct Answer: 12

Explanation:

Capacity of tank = (8 X 18) = 144 litres

If the capacity of each bucket = 12 litres

Then, Nunber of buckets needed = 144 / 12 = 12 buckets

Correct Answer: 20

Explanation:

Let A takes x hours, then B = (x+40) hours

1/x + 1/x+40 = 1/15

x = 20

Correct Answer: 70 hours

Correct Answer: 8

Correct Answer: 7/15

Explanation:

Let S be the sample space

 

Then n(S) = no of ways of drawing 2 balls out of (6+4) = 10 C 2 10 = 10 * 9 2 * 1 =45

 

Let E = event of getting both balls of same colour

 

Then,n(E) = no of ways (2 balls out of six) or (2 balls out of 4)

 

                = 6 C 2 + 4 C 2 =  6 * 5 2 * 1 + 4 * 3 2 * 1= 15+6 = 21

 

Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15

Correct Answer: 3/4

Explanation:

Let A, B, C be the respective events of solving the problem and  A , B , C be the respective events of not solving the problem. Then A, B, C are independent event

? A , B , C are independent events

Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

  P A = 1 2 , P B = 2 3 , P C = 3 4

? P( none  solves the problem) = P(not A) and (not B) and (not C)  

                  =  P A ? B ? C 

                  =  P A P B P C          ? A , B , C a r e I n d e p e n d e n t                       

                  =   1 2 × 2 3 × 3 4  

                  =  1 4  

Hence, P(the problem will be solved) = 1 - P(none solves the problem) 

                =  1 - 1 4= 3/4

Correct Answer: 55/221

Explanation:

We have n(s) = 52 C 2 52 = 52*51/2*1= 1326. 

Let A = event of getting both black cards 

     B = event of getting both queens 

A?B = event of getting queen of black cards 

n(A) = 52 * 51 2 * 1 =  26 C 2 = 325, n(B)= 26 * 25 2 * 1= 4*3/2*1= 6  and  n(A?B) =  4 C 2 = 1 

P(A) = n(A)/n(S) = 325/1326;

P(B) = n(B)/n(S) = 6/1326 and 

P(A?B) = n(A?B)/n(S) = 1/1326 

P(A?B) = P(A) + P(B) - P(A?B) = (325+6-1) / 1326 = 330/1326 = 55/221