Question

Indra has 3 bags such that each bag has 20 g of cashews and 15 g of almonds. She wants to pack them into gift boxes in such a way that each box has the same weight of dry fruits. Find the number of gift boxes if she filled each with the maximum possible weight.

• A. 9
• B. 7
• C. 4
• D. 15

Answer 1

The correct option is B 7

In each bag, indra has 100g cashews and 80g almonds.
So the total weight of cashews 20 x 3 = 60 g
Total weight of almonds = 15 x 3 = 45 g
Since each gift box has the same weight, the weight of each gift box has to be a number that is a factor of both 60 and 45.

We are also told that she fills these boxes with the maximum possible weight.
⇒ The weight of each box = HCF(60, 45)

Factors of 60 = 1, 2, 3, 4, 5, 6, 10,12,15, 20, 30, 60
Factors of 45 = 1, 3, 5, 9, 15, 45
Common factors = 1, 3, 5, 15
⇒ HCF(60, 45) = 15

Each box thus has 15 g of dry fruits.

From each bag, the number of boxes packed will be = 60/15 + 45/15 = 4+3 = 7.