Question

Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns will it take for both the buckets P and Q, having each turn together to fill the empty drum?

a. 30
b. 40
c. 45
d. 90

Answer 1

If both buckets P and Q turn together, it will take 1 turn to fill the drum.

Step-by-step explanation:

Let's assume that the capacity of bucket Q is x units. Since bucket P has thrice the capacity of bucket Q, the capacity of bucket P would be 3x units.

It takes 60 turns for bucket P to fill the empty drum, so in one turn, it fills 1/60th of the drum. Therefore, in one turn, bucket P fills 3x/60th of the drum, and bucket Q fills x/60th of the drum.

To find out how many turns it will take for both buckets P and Q, working together, to fill the drum, we need to add their individual rates of filling. The combined rate is (3x/60) + (x/60) = 4x/60 = x/15.

Therefore, it will take 15/x turns for both buckets P and Q, working together, to fill the drum.

Let's solve the equation 15/x = 1 to find out the value of x. Cross-multiplying, we get 15 = x. Hence, the value of x is 15.

So, it will take 15/15 turns for both buckets P and Q, working together, to fill the empty drum, which simplifies to 1 turn. Therefore, the answer is 1 turn.