Let's go through the question step-by-step and provide detailed answers for each part.
### Part (a)
Mrs. Bhattarai buys 3 bags of rice where each bag weighs 5 kg and costs Rs 600.
#### (i) How many kilograms of rice does she buy?
First, we need to calculate the total weight of the rice that Mrs. Bhattarai buys. Each bag weighs 5 kg, and she buys 3 bags. So, we multiply the number of bags by the weight per bag:
[tex]\[ \text{Total weight} = \text{Number of bags} \times \text{Weight per bag} \][/tex]
[tex]\[ \text{Total weight} = 3 \times 5 \][/tex]
[tex]\[ \text{Total weight} = 15 \, \text{kg} \][/tex]
Mrs. Bhattarai buys 15 kilograms of rice.
#### (ii) What type of proportion are the quantity and cost of rice? Give reason.
In this scenario, the quantity of rice and the cost are directly proportional. This means that as the quantity of rice increases, the cost also increases in a proportional manner. The reason for this is that the cost of the rice depends linearly on the quantity bought. For example, buying 1 bag costs Rs 600, buying 2 bags costs Rs 1200, and buying 3 bags costs Rs 1800. Therefore, this is a direct proportion relationship.
#### (iii) How much money does Mrs. Bhattarai pay to buy 3 bags of rice?
To find the total cost, we multiply the cost per bag by the number of bags bought. Each bag costs Rs 600, and she buys 3 bags:
[tex]\[ \text{Total cost} = \text{Number of bags} \times \text{Cost per bag} \][/tex]
[tex]\[ \text{Total cost} = 3 \times 600 \][/tex]
[tex]\[ \text{Total cost} = 1800 \][/tex]
Mrs. Bhattarai pays Rs 1800 to buy 3 bags of rice.
### Part (b)
Prakash buys copies at a rate of Rs 360 per dozen. We need to determine how many copies he buys for Rs 540.
First, let's determine the cost of a single copy. Since there are 12 copies in a dozen:
[tex]\[ \text{Cost per dozen} = 360 \][/tex]
[tex]\[ \text{Cost per copy} = \frac{360}{12} \][/tex]
[tex]\[ \text{Cost per copy} = 30 \, \text{Rs per copy} \][/tex]
To find out how many copies Prakash can buy for Rs 540:
[tex]\[ \text{Number of copies} = \frac{540}{30} \][/tex]
[tex]\[ \text{Number of copies} = 18 \][/tex]
Prakash buys 18 copies for Rs 540.
