Question

A bag contains tomatoes, potatoes and onions in the ratio \[6:9:5\]. If the weight of these vegetables in the bag is 2 kg, find the weight of each of them.

Answer 1

Hint: Here in this question, we have to find the weight of each vegetable using their ratios. To solve this, let’s take a weight as \[x\]then multiply the height with the ratios of weight of each vegetable and give the total weight of the vegetable in the bag then simplify by using a basic arithmetic operation, we get the required weight.

Complete step-by-step answer:
A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
The most common way to write a ratio using a colon i.e., \[a:b\]
Where, a is antecedent and b is the consequent.
Consider the questions,
Given the ratio of weight of tomatoes, potatoes and onions is \[6:9:5\] respectively.
Total weight of vegetables in the bag is 2 kg.
Now, we have to find the actual weight of each vegetable.
Let’s take a weight as \[x\]
Then the weight of the vegetables are:
Tomatoes\[ = 6x\]
Potatoes\[ = 9x\]
Onions\[ = 5x\]
Given that the total weight of these vegetables in bag is 2 kg i.e.,
\[ \Rightarrow \,\,\,6x + 9x + 5x = 2\]
On adding the like terms, we get
\[ \Rightarrow \,\,\,20x = 2\]
Divide 20 by both side
\[ \Rightarrow \,\,\,x = \dfrac{2}{{20}}\]
On simplification, we get
\[ \Rightarrow \,\,\,x = 0.1\,\,kg\]
Therefore, the weight of vegetables are:
Tomatoes\[ = 6x = 6 \times 0.1 = 0.6\,kg\]or \[600g\]
Potatoes\[ = 9x = 9 \times 0.1 = 0.9\,kg\] or \[900g\]
Onions\[ = 5x = 5 \times 0.1 = 0.5\,kg\] or \[500g\]

Note: Ratio problems are word problems that use ratios to relate or comparison of the different items in the question. Remember The main things to be aware about for ratio problems are Change the quantities to the same unit if necessary and further simplify by the proper arithmetic operations.