Question

Finally Jack reached Cottage city. He went to a restaurant and had a nice meal but couldn’t pay because he had future currency with him. He told politely to the owner- “I am a great mathematician, I am sure I can be of some help to you.” Then, the owner took him to the kitchen and showed 5 containers of different capacity.

$\begin{array}{cc}\text{Container 1}& \text{3 kg}\\ \text{Container 2}& \text{4 kg}\\ \text{Container 3}& \text{5 kg}\\ \text{Container 4}& \text{6 kg}\\ \text{Container 5}& \text{7 kg}\end{array}$

Then he gave Jack a question which was actually a problem he was facing.

“Every container is full of rice. If you take rice out from say Container 1 and 4 alternatively, such that it takes equal number of steps to empty both of them, which of the following measuring cups would you use?”

• A. 1 kg cup with markings per 0.2 kg
• B. 2 kg cup with markings per 0.2 kg
• C. 1 kg cup with markings per 0.8 kg
• D. 2 kg cup with markings per 0.8 kg

Answer 1

The correct option is B

2 kg cup with markings per 0.2 kg

$\begin{array}{cc}\text{Container 1}& \text{3 kg}\\ \text{Container 2}& \text{4 kg}\\ \text{Container 3}& \text{5 kg}\\ \text{Container 4}& \text{6 kg}\\ \text{Container 5}& \text{7 kg}\end{array}$

The total amount of rice that he has = 3 kg + 4 kg + 5 kg + 6 kg + 7 kg = 25 kg

Average amount of rice = $\frac{25kg}{5}$ = 5 kg

So, amount taken out from container 1 (3 kg) in each step = $\frac{3}{5}$ kg = 0.6 kg = 3 $\times$ 0.2 kg

Amount taken out from container 4 (6 kg) in each step = $\frac{6}{5}$ kg = 1.2 kg = 6 $\times$ 0.2 kg

So, a measuring cup with markings at 0.2 kg and size greater than 1 kg will suffice. The correct option is hence B.